{"id":28683,"date":"2023-05-05T03:18:28","date_gmt":"2023-05-05T03:18:28","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=28683"},"modified":"2023-05-10T16:30:43","modified_gmt":"2023-05-10T16:30:43","slug":"zero-product-property-definition-formula-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/zero-product-property","title":{"rendered":"Zero Product Property: Definition, Formula, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-bcfb337d-dea8-4931-9941-7cc45217aa84\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/zero-product-property#0-what-is-the-zero-product-property>What Is the Zero Product Property?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/zero-product-property#3-advantages-of-zero-product-property>Advantages of Zero Product Property<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/zero-product-property#4-disadvantages-of-zero-product-property>Disadvantages of Zero Product Property<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/zero-product-property#7-solved-examples-on-zero-product-property>Solved Examples on Zero Product Property<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/zero-product-property#8-practice-problems-on-zero-product-property>Practice Problems on Zero Product Property<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/zero-product-property#9-frequently-asked-questions-on-zero-product-property>Frequently Asked Questions on Zero Product Property<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-zero-product-property\">What Is the Zero Product Property?<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>The Zero Product Property states that if <\/strong>$a\\times b = 0$<strong>, then we must have <\/strong>$a = 0$<strong> or <\/strong>$b = 0$<strong> or both <\/strong>$a = b = 0$<strong>. It is also known as the \u201czero product principle.\u201d<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Suppose you multiply two real numbers and get 0 as the product, what can you say about the two numbers? What could the numbers be? When the result from multiplying two numbers is zero, the following two cases are possible<\/p>\n\n\n\n<p class=\" eplus-wrapper\">i) one of them is 0<\/p>\n\n\n\n<p class=\" eplus-wrapper\">ii) both of them are 0<\/p>\n\n\n\n<p class=\" eplus-wrapper\">This idea is called the zero product principle. This property is useful in solving the equations of the form $(x + a)(x + b) = 0$.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-using-associative-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_together_we_flee_4_gm.png\" alt=\"Add Using Associative Property Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Using Associative Property Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/apply-distributive-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_facts_mul_dispro_exp1_pt.png\" alt=\"Apply Distributive Property Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Apply Distributive Property Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-word-problems-on-product-of-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_real_life_prob_area_pt.png\" alt=\"Area Word Problems on Product of Fractions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area Word Problems on Product of Fractions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-correct-product-for-the-multiplication-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_mult_match_4dby1d_fluently_pt.png\" alt=\"Choose the Correct Product for the Multiplication Expressions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Correct Product for the Multiplication Expressions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-missing-digit-in-the-product\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_find_missing_diff_arngment_pt.png\" alt=\"Choose the Missing Digit in the Product Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Missing Digit in the Product Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-product-for-the-multiplication-questions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_find_product_4dby1d_1_pt.png\" alt=\"Choose the Product for the Multiplication Questions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Product for the Multiplication Questions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/determine-the-missing-digit-in-the-product\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_find_missing_digit_2_pt.png\" alt=\"Determine the Missing Digit in the Product Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Determine the Missing Digit in the Product Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/divide-using-patterns-of-zeros\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_div_using_zero_a_pt.png\" alt=\"Divide Using Patterns of Zeros Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Divide Using Patterns of Zeros Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/estimate-products-of-2-digit-and-3-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_estimate_product_3d_by_2d_pt.png\" alt=\"Estimate Products of 2-digit and 3-digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Estimate Products of 2-digit and 3-digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/estimate-products-of-two-2-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_estimate_product_2d_by_2d_pt.png\" alt=\"Estimate Products of Two 2-digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Estimate Products of Two 2-digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-zero-product-property\">Zero Product Property<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>If the product of two or more factors equals zero, then at least one of the factors is equal to zero.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">It can be written in symbolic form as:<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$a \\times b = 0 \\Leftrightarrow a = 0$<strong>, or <\/strong>$b = 0$<strong>, or both <\/strong>$a = b = 0$<strong>.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">In other words, the zero product property means that the product of two non-zero real numbers can never be zero.<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-the-numbers-using-commutative-property-of-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-the-numbers-using-commutative-property-of-addition.jpeg\" alt=\"Add the Numbers Using Commutative Property of Addition\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/apply-commutative-property-of-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/apply-commutative-property-of-addition.jpeg\" alt=\"Apply Commutative Property of Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a 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data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/break-multiply-add-using-distributive-property.jpeg\" alt=\"Break Multiply Add using Distributive Property Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/break-using-distributive-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/break-using-distributive-property.jpeg\" alt=\"Break using Distributive Property Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/commutative-property-of-addition-on-number-line\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/commutative-property-of-addition-on-number-line.jpeg\" alt=\"Commutative Property of Addition on Number Line Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/commutative-property-of-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/commutative-property-of-addition.jpeg\" alt=\"Commutative Property of Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container 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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-zero-product-property-in-equations\">Zero Product Property in Equations<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">When solving equations, the zero product property can be used to determine the values of the variables. The zero product property is incredibly useful for resolving quadratic equations in the factored forms.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">We can extend the zero product property and state that&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">If $(x + a)(x + b)(x + c)$&#8230;$(x + n) = 0$, then<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$x + a = 0$ <strong>or<\/strong> $x + b = 0$ <strong>or <\/strong>&#8230; $(x + n)=0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Example 1:<\/strong> if $(x + a) (x + b) = 0$, then by the zero product property, we can say that&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$(x + a) = 0\\; or (x + b) = 0$.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Now, solving each of these for x would give the solutions for the given quadratic equation.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Thus, $x = \\;-a$ or $x = \\;-b$<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Example 2:<\/strong> $x(x + 2) (x + 3) = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">By the zero product property,<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;$x = 0$ or $x + 2 = 0$ or $x + 3 = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Thus, $x = 0$, or $x= \\;-2$, or $x= \\;-3$<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Example 3:<\/strong> $(x \\;-\\; 3) (x + 6) = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Using the zero product property, we know that,<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$(x \\;-\\; 3) = 0$ or&nbsp; $(x + 6) = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$x = 3$ or $x = \\;-\\; 6$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">These are the two solutions of the equation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-advantages-of-zero-product-property\">Advantages of Zero Product Property<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">The zero product property is useful to find values of variables when we have a factored form of the equation. When the product of two or more factors is 0, we can apply the property and simply put each factor equal to 0.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">The zero product property helps in solving the equations of the form $(x + a)(x + b)(x + c)$&#8230;.$(x + n) =0$.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">The zero product property is particularly helpful in solving quadratic equations.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">If we have an equation of the form nx=0, where n is a non-zero real number and x is a variable, we can apply the zero product property and conclude that x=0.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-disadvantages-of-zero-product-property\">Disadvantages of Zero Product Property<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Zero product property cannot be applied to matrices. It means that the product of two non-zero matrices can be 0.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Zero product property is not applicable to the vectors as well. Two non-zero vectors, when multiplied, can result in a zero vector.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">We can apply the zero product property to solve equations if and only if we have the factored form. We must know how to factorize the given equation before we can apply the property.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-facts-about-zero-product-property\">Facts about Zero Product Property<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">The product of two non-zero real numbers can never be 0.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Zero Product Property is also known as zero product principle, zero product property of multiplication, the null factor law, the null factor theorem, the nonexistence of nontrivial zero divisors, the zero product rule.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">The zero product property allows us to factor equations and solve them.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">According to the zero product rule, if the product of any number of expressions is 0, then at least one of them must also be zero.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">You can use the zero product property only if the expression is in the factored form and set to 0.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">The zero product rule is satisfied by the set of real numbers, integers, rational numbers, whole numbers, natural numbers.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">In this article, we have learned about zero product property. The zero product property allows us to factor equations and solve them. Now let&#8217;s solve some zero product property examples and practice problems for better understanding.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-solved-examples-on-zero-product-property\">Solved Examples on Zero Product Property<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>1. Solve the equation using the zero-product property.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">$(\ud835\udc65 \\;\u2212\\; 2)(\ud835\udc65 \\;\u2212\\; 5) = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$(\ud835\udc65 \\;\u2212\\; 2)(\ud835\udc65 \\;\u2212\\; 5) = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">The equation is already in the factored form. So, we will simply apply zero product property to solve the equation.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$\ud835\udc65 \\;\u2212\\;2 = 0$ <strong>or<\/strong> $\ud835\udc65\\;\u2212\\;5 = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$x \\;-\\; 2 + 2 = 0 + 2$&nbsp; <strong>or<\/strong>&nbsp; $x \\;-\\; 5 + 5 = 0 + 5$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$x = 2$ <strong>or<\/strong> $x = 5$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Thus, $x = 2$ or $x = 5$ are the roots.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>2. Solve using the zero product property: <\/strong>$2 x^2 \\;\u2212\\; 3x \\;\u2212\\; 5 = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">We will factorize the equation first.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$2x^2 \\;\u2212\\; 3x \\;\u2212\\; 5 = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$(2\ud835\udc65 \\;\u2212\\; 5)(\ud835\udc65 + 1) = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$2\ud835\udc65 \\;\u2212\\; 5 = 0$ <strong>or<\/strong>&nbsp; $x + 1 = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$2x = 5$&nbsp; <strong>or<\/strong>&nbsp; $x + 1 \\;-\\; 1 = 0 \\;-\\; 1$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$\\frac{2x}{2} = \\frac{5}{2}$&nbsp; <strong>or<\/strong>&nbsp; $x =&nbsp; \\;-\\; 1$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$x = \\frac{5}{2}$&nbsp; <strong>or<\/strong>&nbsp; $x =&nbsp; \\;-\\; 1$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Thus, the solutions are $x = \\frac{5}{2}$ <strong>or<\/strong> $x = \\;-1$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>3. Find the roots of the cubic equation which is in factored form: <\/strong>$(x + 2)^2 (3x + 2)= 0$<strong>.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">We can write the given equation $(x + 2)^2 (3x + 2)= 0$<strong> <\/strong>as&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$(x + 2)( x + 2)(3x + 2) = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">By the zero product property, we have $-\\; 2$, and $-\\; 23$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>4. What is the value of x if <\/strong>$99x = 0$<strong>?<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">The zero product property says that if the product of two numbers is 0, then at least one of the numbers is 0.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">We have $99x = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Here, 99 is a constant.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$99 \\neq 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Thus, by the zero product property, we have $x = 0$<strong>.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>5. Using the zero product property, solve the following for x.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">$10x(x + 2)(x \\;-\\; 5)(4x + 12)$<strong><br><\/strong><br><strong>Solution: <br><\/strong>If $10x(x + 2)(x \\;-\\; 5)(4x + 12)= 0$, at least one of the factors is 0.<\/p>\n\n\n\n<figure class=\"wj-custom-table wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><tbody><tr><td>i) $10x = 0$<br>$\\Rightarrow x = 0$<\/td><td>ii) $x + 2 = 0$<br>$\\Rightarrow x + 2 \\;-\\; 2 = 0 \\;-\\; 2$<br>$\\Rightarrow x + 0 = \\;-\\;2$<br>$\\Rightarrow x = \\;-2$<\/td><\/tr><tr><td>iii) $x \\;-\\; 5 = 0$<br>$\\Rightarrow x \\;-\\; 5 + 5 = 0 + 5$<br>$\\Rightarrow x + 0 = 0 + 5$<br>$\\Rightarrow x = 5$<\/td><td>iv) $4x + 12 = 0$<br>$\\Rightarrow 4x + 12 \\;-\\;12 = 0 \\;-\\; 12$<br>$\\Rightarrow 4x + 0 = \\;-12$<br>$\\Rightarrow 4x = \\;-12$<br>$\\Rightarrow \\frac{4x}{4} = \\;- \\frac{12}{4}$<br>$\\Rightarrow x = \\;-\\; 3$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">The possible roots to the equation are $0,\\; -\\;2,\\; 5,\\; -\\; 3$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-practice-problems-on-zero-product-property\">Practice Problems on Zero Product Property<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Zero Product Property: Definition, Formula, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">If a.b $= 0$, then $a = 0$ or $b = 0$ or $a = b = 0$. <\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Zero Property<\/div><div class=\"spq_answer_block\" data-value=\"1\">Zero Product Property<\/div><div class=\"spq_answer_block\" data-value=\"2\">Multiplication Rule<\/div><div class=\"spq_answer_block\" data-value=\"3\">Both b and c<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Zero Product Property<br\/>According to zero product property, if $\ud835\udc4e \\times \ud835\udc4f = 0$ then either $\ud835\udc4e = 0$ or $\ud835\udc4f = 0$ or both a and b are equal to zero.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">If $5 \\times x = 0$ then, _________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$x \\neq 0$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$x = 0$<\/div><div class=\"spq_answer_block\" data-value=\"2\">x may or may not be equal to 0<\/div><div class=\"spq_answer_block\" data-value=\"3\">$x = \\;-5$ or $x = \\frac{1}{5}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $x = 0$<br\/>If $5 \\times x = 0$ then, the value of x must be zero. <\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Solve for x:<br>$(x + 2)(x \\;-\\; 3) = 0$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$2,\\; 3$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-\\; 2,\\; -\\; 3$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$-\\; 2,\\; 3$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$2,\\; -\\; 3$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $-\\; 2,\\; 3$<br\/>$(x + 2)(x \\;-\\; 3) = 0$.<br>\r\n$x + 2 = 0$ or $x \\;-\\; 3 = 0$<br>\r\nThus, $x = \\;-\\; 2$ or $x = 3$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The product of two non-zero real numbers is<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">never 0<\/div><div class=\"spq_answer_block\" data-value=\"1\">always 0<\/div><div class=\"spq_answer_block\" data-value=\"2\">always positive<\/div><div class=\"spq_answer_block\" data-value=\"3\">always negative<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: never 0<br\/>The product of two non-zero real numbers can never be 0.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The zero product property states that for any real numbers and b, if $ab = 0$, then<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$a = 0$, or $b = 0$, or both $a = b = 0$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$a = 0$ and $b \\neq 0$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$a = b = 0$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$b = 0$ and $a \\neq 0$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $a = 0$, or $b = 0$, or both $a = b = 0$<br\/>For any real numbers a and b, if $ab = 0$, then, either $a = 0$, or $b = 0$, or both a and b equal to zero<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Zero Product Property: Definition, Formula, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Zero Product Property\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    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\"Comment\",\n                                    \"text\": \"According to zero product property, if $$\ud835\udc4e \\\\times \ud835\udc4f = 0$$ then either $$\ud835\udc4e = 0$$ or $$\ud835\udc4f = 0$$ or both a and b are equal to zero. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Multiplication Rule\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to zero product property, if $$\ud835\udc4e \\\\times \ud835\udc4f = 0$$ then either $$\ud835\udc4e = 0$$ or $$\ud835\udc4f = 0$$ or both a and b are equal to zero. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Both b and c\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to zero product property, if $$\ud835\udc4e \\\\times \ud835\udc4f = 0$$ then either $$\ud835\udc4e = 0$$ or $$\ud835\udc4f = 0$$ or both a and b are equal to zero. \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Zero Product Property\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to zero product property, if $$\ud835\udc4e \\\\times \ud835\udc4f = 0$$ then either $$\ud835\udc4e = 0$$ or $$\ud835\udc4f = 0$$ or both a and b are equal to zero. \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to zero product property, if $$\ud835\udc4e \\\\times \ud835\udc4f = 0$$ then either $$\ud835\udc4e = 0$$ or $$\ud835\udc4f = 0$$ or both a and b are equal to zero. \"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If $$5 \\\\times x = 0$$ then, _________.\",\n                    \"text\": \"If $$5 \\\\times x = 0$$ then, _________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If $$5 \\\\times x = 0$$ then, the value of x must be zero. \"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x \\\\neq 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If $$5 \\\\times x = 0$$ then, the value of x must be zero. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"x may or may not be equal to 0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If $$5 \\\\times x = 0$$ then, the value of x must be zero. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x = \\\\;-5$$ or $$x = \\\\frac{1}{5}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If $$5 \\\\times x = 0$$ then, the value of x must be zero. \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$x = 0$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If $$5 \\\\times x = 0$$ then, the value of x must be zero. \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If $$5 \\\\times x = 0$$ then, the value of x must be zero. \"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Solve for x:<br>$$(x + 2)(x \\\\;-\\\\; 3) = 0$$\",\n                    \"text\": \"Solve for x:<br>$$(x + 2)(x \\\\;-\\\\; 3) = 0$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$(x + 2)(x \\\\;-\\\\; 3) = 0$$.<br>\r\n$$x + 2 = 0$$ or $$x \\\\;-\\\\; 3 = 0$$<br>\r\nThus, $$x = \\\\;-\\\\; 2$$ or $$x = 3$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2,\\\\; 3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(x + 2)(x \\\\;-\\\\; 3) = 0$$.<br>\r\n$$x + 2 = 0$$ or $$x \\\\;-\\\\; 3 = 0$$<br>\r\nThus, $$x = \\\\;-\\\\; 2$$ or $$x = 3$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-\\\\; 2,\\\\; -\\\\; 3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(x + 2)(x \\\\;-\\\\; 3) = 0$$.<br>\r\n$$x + 2 = 0$$ or $$x \\\\;-\\\\; 3 = 0$$<br>\r\nThus, $$x = \\\\;-\\\\; 2$$ or $$x = 3$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2,\\\\; -\\\\; 3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(x + 2)(x \\\\;-\\\\; 3) = 0$$.<br>\r\n$$x + 2 = 0$$ or $$x \\\\;-\\\\; 3 = 0$$<br>\r\nThus, $$x = \\\\;-\\\\; 2$$ or $$x = 3$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$-\\\\; 2,\\\\; 3$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$(x + 2)(x \\\\;-\\\\; 3) = 0$$.<br>\r\n$$x + 2 = 0$$ or $$x \\\\;-\\\\; 3 = 0$$<br>\r\nThus, $$x = \\\\;-\\\\; 2$$ or $$x = 3$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$(x + 2)(x \\\\;-\\\\; 3) = 0$$.<br>\r\n$$x + 2 = 0$$ or $$x \\\\;-\\\\; 3 = 0$$<br>\r\nThus, $$x = \\\\;-\\\\; 2$$ or $$x = 3$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The product of two non-zero real numbers is\",\n                    \"text\": \"The product of two non-zero real numbers is\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The product of two non-zero real numbers can never be 0.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"always 0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The product of two non-zero real numbers can never be 0.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"always positive\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The product of two non-zero real numbers can never be 0.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"always negative\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The product of two non-zero real numbers can never be 0.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"never 0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The product of two non-zero real numbers can never be 0.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The product of two non-zero real numbers can never be 0.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The zero product property states that for any real numbers and b, if $$ab = 0$$, then\",\n                    \"text\": \"The zero product property states that for any real numbers and b, if $$ab = 0$$, then\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"For any real numbers a and b, if $$ab = 0$$, then, either $$a = 0$$, or $$b = 0$$, or both a and b equal to zero\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a = 0$$ and $$b \\\\neq 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"For any real numbers a and b, if $$ab = 0$$, then, either $$a = 0$$, or $$b = 0$$, or both a and b equal to zero\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a = b = 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"For any real numbers a and b, if $$ab = 0$$, then, either $$a = 0$$, or $$b = 0$$, or both a and b equal to zero\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$b = 0$$ and $$a \\\\neq 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"For any real numbers a and b, if $$ab = 0$$, then, either $$a = 0$$, or $$b = 0$$, or both a and b equal to zero\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$a = 0$$, or $$b = 0$$, or both $$a = b = 0$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"For any real numbers a and b, if $$ab = 0$$, then, either $$a = 0$$, or $$b = 0$$, or both a and b equal to zero\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"For any real numbers a and b, if $$ab = 0$$, then, either $$a = 0$$, or $$b = 0$$, or both a and b equal to zero\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-frequently-asked-questions-on-zero-product-property\">Frequently Asked Questions on Zero Product Property<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\"><strong>What is the associative property of multiplication?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\">\n\n<p class=\" eplus-wrapper\">According to the associative property of multiplication, the product of any three numbers remains the same, irrespective of the order in which they are grouped.$a\\times(b\\times c) = (a\\times b) c$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\"><strong>What is the identity property of multiplication?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\">\n\n<p class=\" eplus-wrapper\">The identity property of multiplication states that the product of any real number with 1 is always the number itself. The number 1 is called the multiplicative identity.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\"><strong>Why is the zero product property not applicable for matrices ?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\">\n\n<p class=\" eplus-wrapper\">For matrices, the zero product property is not applicable, because if the product of two matrices is a zero matrix, then it is not compulsory that one of the matrices should be a zero matrix.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\"><strong>What is the additive identity for real numbers?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\">\n\n<p class=\" eplus-wrapper\">0 is the additive identity for the set of real numbers. Addition of any real number with 0 is the number itself.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\"><strong>How to apply the zero product property?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-06c84972-7cbb-4ec1-8e3d-3b02fc29ec7c\">\n\n<p class=\" eplus-wrapper\">To apply the zero product property, we set each factor equal to zero and solve for the variable. The zero product property can be applied when the product of the expressions is equal to zero.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Zero Product Property? The Zero Product Property states that if $a\\times b = 0$, then we must have $a = 0$ or $b = 0$ or both $a = b = 0$. It is also known as the \u201czero product principle.\u201d Suppose you multiply two real numbers and get 0 as the &#8230; <a title=\"Zero Product Property: Definition, Formula, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/zero-product-property\" aria-label=\"More on Zero Product Property: Definition, Formula, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-28683","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28683","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=28683"}],"version-history":[{"count":22,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28683\/revisions"}],"predecessor-version":[{"id":29021,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28683\/revisions\/29021"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=28683"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=28683"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=28683"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}