{"id":32434,"date":"2023-08-01T10:18:15","date_gmt":"2023-08-01T10:18:15","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=32434"},"modified":"2023-08-01T10:26:52","modified_gmt":"2023-08-01T10:26:52","slug":"polynomial-in-standard-form-definition-solved-examples-facts-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/polynomial-in-standard-form","title":{"rendered":"Polynomial in Standard Form &#8211; Definition, Solved Examples, Facts, FAQs"},"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-bbd0c430-46fd-4a20-90e2-9247fa0bb81e\" 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\/polynomial-in-standard-form#0-what-is-polynomial-in-standard-form>What Is Polynomial in Standard Form?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/polynomial-in-standard-form#4-how-to-write-a-polynomial-in-standard-form>How to Write a Polynomial in Standard Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/polynomial-in-standard-form#5-addition-and-subtraction-of-standard-form-of-polynomial>Addition and Subtraction of Standard Form of Polynomial<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/polynomial-in-standard-form#8-solved-examples-on-polynomials-in-standard-form>Solved Examples on Polynomials in Standard Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/polynomial-in-standard-form#9-practice-problems-on-polynomials-in-standard-form>Practice Problems on Polynomials in Standard Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/polynomial-in-standard-form#10-frequently-asked-questions-on-polynomials-in-standard-form>Frequently Asked Questions on Polynomials in Standard Form<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-polynomial-in-standard-form\">What Is Polynomial in Standard Form?<\/h2>\n\n\n\n<p><strong>The standard form of a polynomial or a polynomial in the standard form refers to a polynomial whose <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/term\"><strong>terms<\/strong><\/a><strong> are written in the <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/descending-order\"><strong>descending order<\/strong><\/a><strong> of the degree of the <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/variable\"><strong>variables <\/strong><\/a><strong>(highest to lowest).<\/strong><strong><br><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Example of standard form of<\/strong><br><strong>a polynomial<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Non-example of standard form of<\/strong><br><strong>a polynomial<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">$2x^{2} + 5x\\;-\\;1$<\/td><td class=\"has-text-align-left\" data-align=\"left\">$5x\\;-\\;1 + 2x^{2}$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>In the standard form, the highest degree term is placed at the beginning of the polynomial followed by other terms in the decreasing order of degree. Terms are in the decreasing exponential value.<\/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-multiples-of-100-in-unit-form\" 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_pv_add_multiples_100_pt.png\" alt=\"Add Multiples of 100 in Unit Form 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 Multiples of 100 in Unit Form 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\/change-decimals-from-word-form-to-fraction-form\" 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\/decimals_convert_words_to_frac_tenths_pt.png\" alt=\"Change Decimals from Word Form to Fraction Form 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\">Change Decimals from Word Form to Fraction Form 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\/change-expanded-to-standard-form\" 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\/place_value_expand_to_std_5d_pt.png\" alt=\"Change Expanded to Standard Form 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\">Change Expanded to Standard Form 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\/change-to-standard-form\" 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\/place_value_write_in_word_5d_pt.png\" alt=\"Change to Standard Form 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\">Change to Standard Form 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-standard-form-of-the-decomposed-hundredths\" 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\/decimals_compose_hundredths_pt.png\" alt=\"Choose the Correct Standard Form of the Decomposed Hundredths 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 Standard Form of the Decomposed Hundredths 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-standard-form-of-the-decomposed-decimal-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\/decimals_convert_to_standard_form_pt.png\" alt=\"Choose the Standard Form of the Decomposed Decimal 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\">Choose the Standard Form of the Decomposed Decimal 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\/complete-the-expanded-decimal-form\" 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\/decimals_complete_expanded_dec_form_pt.png\" alt=\"Complete the Expanded Decimal Form 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\">Complete the Expanded Decimal Form 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\/complete-the-expanded-form\" 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\/place_value_complete_expanded_form_pt.png\" alt=\"Complete the Expanded Form 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\">Complete the Expanded Form 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\/complete-the-expanded-form-of-decimal-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\/decimals_complete_expanded_form_pt.png\" alt=\"Complete the Expanded Form of Decimal 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\">Complete the Expanded Form of Decimal 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\/complete-the-expanded-form-of-whole-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\/place_value_write_expended_form_pt.png\" alt=\"Complete the Expanded Form of Whole 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\">Complete the Expanded Form of Whole 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\" id=\"1-meaning-of-polynomial-in-standard-form\">Meaning of Polynomial in Standard Form<\/h2>\n\n\n\n<p>The terms of the polynomial in standard form are organized from highest degree to lowest degree, which helps in simplifying and performing various operations on polynomials.<\/p>\n\n\n\n<p>A polynomial is said to be in its standard form if it is written in such a way that the term with the highest degree is placed at the beginning, followed by the term having the next highest degree, and so on. In other words, the degree of terms decreases as you go from left to right.<\/p>\n\n\n\n<p><strong>Example:<\/strong> $x^{7} + 5x^{6}\\;-\\;2x^{5} + 5x^{4} + x^{3}\\;-\\;3x^{2} + 9x + 2$<\/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\/color-animals-and-trace-word-forms-within-10\" 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\/color-animals-and-trace-word-forms-within-10.jpeg\" alt=\"Color Animals and Trace Word Forms (Within 10)\">\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\/color-animals-and-trace-word-forms-within-5\" 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\/color-animals-and-trace-word-forms-within-5.jpeg\" alt=\"Color Animals and Trace Word Forms (Within 5)\">\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\/color-birds-and-trace-word-forms-within-10\" 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\/color-birds-and-trace-word-forms-within-10.jpeg\" alt=\"Color Birds and Trace Word Forms (Within 10)\">\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\/color-birds-and-trace-word-forms-within-5\" 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\/color-birds-and-trace-word-forms-within-5.jpeg\" alt=\"Color Birds and Trace Word Forms (Within 5)\">\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\/color-dinosaurs-and-trace-word-forms-within-10\" 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\/color-dinosaurs-and-trace-word-forms-within-10.jpeg\" alt=\"Color Dinosaurs and Trace Word Forms (Within 10)\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div 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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\/color-flowers-and-trace-word-forms-within-10.jpeg\" alt=\"Color Flowers and Trace Word Forms (Within 10)\">\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\/color-flowers-and-trace-word-forms-within-5\" 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\/color-flowers-and-trace-word-forms-within-5.jpeg\" alt=\"Color Flowers and Trace Word Forms (Within 5)\">\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\/color-food-items-and-trace-word-forms-within-10\" 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\/color-food-items-and-trace-word-forms-within-10.jpeg\" alt=\"Color Food Items and Trace Word Forms (Within 10)\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" 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to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-polynomial-in-standard-form-definition\">Polynomial in Standard Form Definition<\/h2>\n\n\n\n<p><strong>Standard form of a polynomial is a way of writing a polynomial where the terms are arranged in descending order of degree. A polynomial in standard form is a polynomial written such that its exponents are in descending order.&nbsp;<\/strong><\/p>\n\n\n\n<p>The standard form of a polynomial with degree n is given by<\/p>\n\n\n\n<p>$a_{n}x^{n} + a_{n-1}x^{n-1} +$ . . .$+ a_{1}x + a_{0}$<\/p>\n\n\n\n<p>(<strong>Note<\/strong>: The first term of a polynomial in standard form, the term containing the highest degree, is called the leading term.)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-standard-form-of-polynomial-degree\">Standard Form of Polynomial &#8211; Degree<\/h2>\n\n\n\n<p>When the polynomial is written in the standard form, the degree of the polynomial is simply the degree of the first term.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Polynomial in the standard form<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Degree<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">$3x^{3}\\;-\\;2x + 1$<\/td><td class=\"has-text-align-left\" data-align=\"left\">3<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">$x^{2}\\;y^{3}\\;-\\;2xy + x$<\/td><td class=\"has-text-align-left\" data-align=\"left\">5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The degree of a polynomial with a single variable can be defined as the highest exponent of the variable present in the variable. In the polynomial constituting multiple variables, the degree is calculated by finding the sum of the exponents of variables in each term and then comparing to find the highest degree.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"326\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/degree-of-polynomial-with-multiple-variables.png\" alt=\"Degree of polynomial with multiple variables\" class=\"wp-image-32451\" title=\"Degree of polynomial with multiple variables\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/degree-of-polynomial-with-multiple-variables.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/degree-of-polynomial-with-multiple-variables-300x158.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-how-to-write-a-polynomial-in-standard-form\">How to Write a Polynomial in Standard Form<\/h2>\n\n\n\n<p>Let\u2019s understand the steps to convert a polynomial to standard form.<\/p>\n\n\n\n<p><strong>Step 1: <\/strong>Add or subtract the like terms (if any) to identify the total number of terms present in the polynomial. Note down the degree of each term.<\/p>\n\n\n\n<p><strong>Step 2: <\/strong>Write the term with the highest degree in the beginning.<\/p>\n\n\n\n<p><strong>Step 3: <\/strong>Arrange the terms in descending order of the degree. Do not forget to take along the signs attached to each term. Place the mathematical operators carefully.<\/p>\n\n\n\n<p><strong>Step 4:<\/strong> The constant or 0-degree term will come in the end.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-addition-and-subtraction-of-standard-form-of-polynomial\">Addition and Subtraction of Standard Form of Polynomial<\/h2>\n\n\n\n<p>Writing polynomials in standard form helps us to identify the like terms in the given polynomials, which makes the addition or subtraction of polynomials much easier.<\/p>\n\n\n\n<p>Two or more terms are called like terms if they have the same variable (or variables) with the same exponent. The important rule when adding or subtracting polynomial expressions is, we can only add or subtract like terms.<\/p>\n\n\n\n<p><strong>Example:<\/strong> $\\;-\\;4x^{3}\\;y$ and $6x^{3}\\;y$ are like terms.<\/p>\n\n\n\n<p><strong>Steps for the Addition of Polynomials<\/strong><\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Write the polynomials in standard form.<\/p>\n\n\n\n<p><strong>Step 2: <\/strong>Write both the polynomials vertically to align the like terms (in case of no extra term). The polynomials can also be added horizontally, where like terms must be grouped for ease of calculation.&nbsp;<\/p>\n\n\n\n<p><strong>Step 3:<\/strong> Perform the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/addition\">addition<\/a> according to the signs.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th><strong>Vertical addition<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Horizontal addition<\/strong><\/th><\/tr><\/thead><tbody><tr><td><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"111\" class=\"wp-image-32442\" style=\"width: 150px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-addition-of-polynomials-using-the-standard-form.png\" alt=\"Vertical addition of polynomials using the standard form\"><\/td><td class=\"has-text-align-left\" data-align=\"left\">$(6p^{3} \\;-\\; p^{2} + 2) + (2p^{3} + 8p^{2} \\;-\\; 2)$<br>$= 6p^{3} + 2p^{3} + 8p^{2}\\;-\\; p^{2} \\;-\\; 2 + 2$<br>$= 8p^{3} + 7p^{2}$&nbsp;<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Steps for the Subtraction of Polynomials<\/strong><\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Write the polynomial in standard form.<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Write the polynomials vertically (one below the other) such that terms are aligned. You can also write them horizontally and group the like terms.<\/p>\n\n\n\n<p><strong>Step 3: <\/strong>To <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/subtraction\/subtract\">subtract<\/a>, reverse the sign of each term in the second polynomial and add the two polynomials. Follow the sign convention while adding.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Vertical Subtraction<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Horizontal subtraction<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"88\" class=\"wp-image-32447\" style=\"width: 150px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-subtraction-of-polynomials-using-the-standard-form.png\" alt=\"Vertical subtraction of polynomials using the standard form\"><\/td><td class=\"has-text-align-left\" data-align=\"left\">$4x^{4} \\;-\\; 3x^{2} + 2x \\;-\\; (2x^{4} + x^{2} + x)$<br>$= 4x^{4} \\;-\\; 3x^{2} + 2x \\;-\\; 2x^{4} \\;-\\; x^{2} \\;-\\; x$<br>$= 4x^{4} \\;-\\; 2x^{4} \\;-\\; 3x^{2} \\;-\\; x^{2} + 2x \\;-\\; x$<br>$=2x^{4} \\;-\\; 4x^{2} + x$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-facts-about-polynomials-in-standard-form\">Facts about Polynomials in Standard Form<\/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=\"wp-block-list\">\n<li>The standard form of every polynomial is unique and specific for that polynomial.&nbsp;<\/li>\n\n\n\n<li>The degree of the polynomial written in the standard form is the degree of the first term (leading term).<\/li>\n\n\n\n<li>The first term in the standard form of polynomial is called the leading term and its coefficient is called the leading coefficient.&nbsp;<\/li>\n\n\n\n<li>To simplify a polynomial in the standard form, combine like terms for addition\/subtraction, and rearrange the terms in descending order of degree.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-conclusion\"><br>Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about the standard form of a polynomial. Let\u2019s solve a few examples and practice problems for better understanding and clarity.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-solved-examples-on-polynomials-in-standard-form\">Solved Examples on Polynomials in Standard Form<\/h2>\n\n\n\n<p><strong>1. Convert the polynomial to standard form:&nbsp; <\/strong>$\\;-\\;3x^{2} + x^{4}\\;-\\; 5x + 5x^{3}+ 1$.<\/p>\n\n\n\n<p><strong>Solution:<\/strong> There are 5 terms.<\/p>\n\n\n\n<p>Degree of $3x^{2} = 2$<\/p>\n\n\n\n<p>Degree of $x^{4} = 4$<\/p>\n\n\n\n<p>Degree of $5x = 1$<\/p>\n\n\n\n<p>Degree of $5x^{3} = 3$<\/p>\n\n\n\n<p>Degree of $1 = 0$<\/p>\n\n\n\n<p>A polynomial in standard form is written by arranging terms in the descending order of the degree.&nbsp;<\/p>\n\n\n\n<p>Polynomial in the standard form: $x^{4} + 5x^{3}\\;-\\; 3x^{2} \\;-\\;5x +1 = 0$.&nbsp;<\/p>\n\n\n\n<p><strong>2. What is the degree of a polynomial <\/strong>$5x^{3} + xy^{4} \\;-\\; 3xy^{2} \\;-\\; 4$?<strong> Write it in the standard form.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>The degree of the polynomial will be calculated for each term as follows:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td>Term<\/td><td>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; $xy^{4}$<\/td><td>$3xy^{2}$<\/td><td>$5x^{3}$<\/td><td>4<\/td><\/tr><tr><td>Degree<\/td><td>$1 + 4 = 5$<\/td><td>$1 + 2 = 3$<\/td><td>3<\/td><td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>In the standard form, we can write the given polynomial as<\/p>\n\n\n\n<p>$xy^{4} + 5x^{3}\\;-\\; 3xy^{2} \\;-\\; 4$<\/p>\n\n\n\n<p>The term xy4 has the highest sum of exponents. Thus, the degree of the polynomial is 5.&nbsp;<\/p>\n\n\n\n<p><strong>3. Add the following polynomials: <\/strong>$p(x) = 3x^{2} + 2x^{3} \\;-\\; 5$<strong> and <\/strong>$q(x) = 12x^{2} + 3x^{3} \\;- \\;1$.<\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>Rewrite the polynomials in the standard form.<\/p>\n\n\n\n<p>$p(x) = 2x^{3} + 3x^{2} \\;-\\; 5$<\/p>\n\n\n\n<p>$q(x) = 3x^{3} +12x^{2} \\;-\\; 1$<\/p>\n\n\n\n<p>$p(x) + q(x) = (2x^{3} + 3x^{2} \\;-\\; 5) + (3x^{3} + 12x^{2}\\;-\\; 1)$&nbsp;<\/p>\n\n\n\n<p>$p(x) + q(x) = 5x^{3} + 15x^{2} \\;-\\; 6$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-practice-problems-on-polynomials-in-standard-form\">Practice Problems on Polynomials in Standard Form<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Polynomial in Standard Form - Definition, Solved Examples, Facts, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which terms in polynomials do not contain variables?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Leading term<\/div><div class=\"spq_answer_block\" data-value=\"1\">Leading coefficient<\/div><div class=\"spq_answer_block\" data-value=\"2\">Constant<\/div><div class=\"spq_answer_block\" data-value=\"3\">Fourth term<\/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: Constant<br\/>Constant term does not contain variables.<\/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\">Which polynomial is in the standard form?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$15x^{5} + 12x^{7}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\;-\\;15x^{5} + 12x^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$15x\\;-\\; 12x^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$15x^{2} \\;-\\; 6x^{3}$<\/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: $\\;-\\;15x^{5} + 12x^{3}$<br\/>$\\;-\\;15x^{5} + 12x^{3}$ is written using the descending order of the exponents.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">What is the degree of the polynomial: $\\;-\\;18x^{5} + 3x^{3} + 2x^{2}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5<\/div><div class=\"spq_answer_block\" data-value=\"1\">3<\/div><div class=\"spq_answer_block\" data-value=\"2\">18<\/div><div class=\"spq_answer_block\" data-value=\"3\">10<\/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: 5<br\/>Highest power of a variable is 5.<\/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 degree of the polynomial in the standard form is the<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">degree of the leading term<\/div><div class=\"spq_answer_block\" data-value=\"1\">constant<\/div><div class=\"spq_answer_block\" data-value=\"2\">coefficient of the leading term<\/div><div class=\"spq_answer_block\" data-value=\"3\">coefficient of x<\/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: degree of the leading term<br\/>The degree of the polynomial in the standard form is the degree of the leading term.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Which polynomials are in standard form?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$a^{3} \\;-\\; b^{5} + 2$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\;-\\;3xy^{2} + 7xy \\;-\\; 2$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$p^{2} \\;-\\; q^{4} + 2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$u^{2} \\;-\\; v^{3} + 2uv$<\/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: $\\;-\\;3xy^{2} + 7xy \\;-\\; 2$<br\/>The highest degree term must be placed first, followed by the lower degree terms.<\/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\": \"Polynomial in Standard Form - Definition, Solved Examples, Facts, FAQs\",        \n    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\"text\/html\",\n                                \"text\": \"Fourth term\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Constant term does not contain variables.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Constant\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Constant term does not contain variables.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Constant term does not contain variables.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which polynomial is in the standard form?\",\n                    \"text\": \"Which polynomial is in the standard form?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\;-\\\\;15x^{5} + 12x^{3}$$ is written using the descending order of the exponents.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$15x^{5} + 12x^{7}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\;-\\\\;15x^{5} + 12x^{3}$$ is written using the descending order of the exponents.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$15x\\\\;-\\\\; 12x^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\;-\\\\;15x^{5} + 12x^{3}$$ is written using the descending order of the exponents.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$15x^{2} \\\\;-\\\\; 6x^{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\;-\\\\;15x^{5} + 12x^{3}$$ is written using the descending order of the exponents.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\;-\\\\;15x^{5} + 12x^{3}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\;-\\\\;15x^{5} + 12x^{3}$$ is written using the descending order of the exponents.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\;-\\\\;15x^{5} + 12x^{3}$$ is written using the descending order of the exponents.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the degree of the polynomial: $$\\\\;-\\\\;18x^{5} + 3x^{3} + 2x^{2}$$?\",\n                    \"text\": \"What is the degree of the polynomial: $$\\\\;-\\\\;18x^{5} + 3x^{3} + 2x^{2}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Highest power of a variable is 5.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Highest power of a variable is 5.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"18\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Highest power of a variable is 5.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Highest power of a variable is 5.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Highest power of a variable is 5.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Highest power of a variable is 5.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The degree of the polynomial in the standard form is the\",\n                    \"text\": \"The degree of the polynomial in the standard form is the\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The degree of the polynomial in the standard form is the degree of the leading term.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"constant\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The degree of the polynomial in the standard form is the degree of the leading term.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"coefficient of the leading term\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The degree of the polynomial in the standard form is the degree of the leading term.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"coefficient of x\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The degree of the polynomial in the standard form is the degree of the leading term.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"degree of the leading term\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The degree of the polynomial in the standard form is the degree of the leading term.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The degree of the polynomial in the standard form is the degree of the leading term.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which polynomials are in standard form?\",\n                    \"text\": \"Which polynomials are in standard form?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The highest degree term must be placed first, followed by the lower degree terms.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a^{3} \\\\;-\\\\; b^{5} + 2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The highest degree term must be placed first, followed by the lower degree terms.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$p^{2} \\\\;-\\\\; q^{4} + 2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The highest degree term must be placed first, followed by the lower degree terms.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$u^{2} \\\\;-\\\\; v^{3} + 2uv$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The highest degree term must be placed first, followed by the lower degree terms.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\;-\\\\;3xy^{2} + 7xy \\\\;-\\\\; 2$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The highest degree term must be placed first, followed by the lower degree terms.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The highest degree term must be placed first, followed by the lower degree terms.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-frequently-asked-questions-on-polynomials-in-standard-form\">Frequently Asked Questions on Polynomials in Standard Form<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\" 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-0-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\"><strong>Can variables in polynomials have fractional or negative exponents?<\/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-0-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\">\n\n<p>No. Exponents of the variables in polynomials cannot be fractional or negative. Coefficients of variables can be fractions.<\/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-1-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\"><strong>Can polynomials have an infinite number of terms?<\/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-1-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\">\n\n<p>A polynomial cannot have an infinite number of terms.<\/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-2-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\"><strong>How to write the standard form of a polynomial having two variables?<\/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-2-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\">\n\n<p>Find the degree of each term by adding exponents of the variables. Arrange the terms by the descending order of the degree.<\/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-3-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\"><strong>What is a homogeneous polynomial?<\/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-3-21cd6549-dfe1-4a9d-a42b-5baa6ab8a9e6\">\n\n<p>When each term of the polynomial (each monomial) has the same degree, it is a homogeneous polynomial.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Polynomial in Standard Form? The standard form of a polynomial or a polynomial in the standard form refers to a polynomial whose terms are written in the descending order of the degree of the variables (highest to lowest). Example of standard form ofa polynomial Non-example of standard form ofa polynomial $2x^{2} + 5x\\;-\\;1$ &#8230; <a title=\"Polynomial in Standard Form &#8211; Definition, Solved Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/polynomial-in-standard-form\" aria-label=\"More on Polynomial in Standard Form &#8211; Definition, Solved Examples, Facts, FAQs\">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-32434","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\/32434","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=32434"}],"version-history":[{"count":16,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32434\/revisions"}],"predecessor-version":[{"id":32455,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32434\/revisions\/32455"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=32434"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=32434"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=32434"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}