## What Is a Constant Polynomial?

A constant polynomial is a polynomial with only a constant term and no variable. It is a polynomial expression with only a single term, which is a constant.

We express a constant polynomial as $P(x) = c$, where c is a constant.

**Constant polynomial examples:**

- $f(x) = 5$
- $p(x) = 1$
- $g(x) = 0.5$

Note that f(x)=0 is a special case of a constant polynomial and it is called a zero polynomial.

## Constant Polynomial Definition

A constant polynomial is a polynomial of the form $P(x) = c$, for all real x, where c is a constant (a real number).

## Degree of a Constant Polynomial

The degree of a constant polynomial is 0. The degree represents the highest power of the variable present in a polynomial.

We can represent the polynomial $P(x) = c$ as $P(x) = c.x0$

Thus, the degree of a constant polynomial is 0 regardless of the constant present.

**Note: **If $c = 0$, we get a zero polynomial $P(x) = 0$ and the degree of a zero polynomial is not defined.

## Constant Polynomial Graph

The graph of a **constant polynomial** is a horizontal line parallel to the x-axis. Since the value of the polynomial remains the same regardless of the variable, the graph remains at a constant height above or below the x-axis, depending on the value of the constant.

For example, the **constant polynomial** $P(x) = 5$ graph is a straight line parallel to the x-axis at $y = 5$.

## Difference between Constant Polynomial and Zero Polynomial

Constant Polynomial | Zero Polynomial |
---|---|

Degree $= 0$ | Degree is not defined. |

It is of the form $P(x) = c$, where c is a real number. | It is of the form $P(x) = 0$. |

Its graph is a horizontal line parallel to the x-axis. | Its graph is the x-axis. |

For a constant polynomial function, Domain $= R$ Range $= \left\{c\right\}$ | For a zero polynomial function, $Domain = R$ $Range = \left\{0\right\}$ |

We get a constant polynomial, when the degree of each term (each monomial) is 0. | We get a zero polynomial, when the coefficients of all variables are 0. |

## Facts about Constant Polynomials:

- The degree of constant polynomials is always 0.
- Constant polynomials are also called degree-0 polynomials.
- The graph of a
**constant polynomial**is a horizontal line parallel to the x-axis. - Constant polynomials are not affected by changes in the variable.
- Addition of two constant polynomials is always a constant polynomial.

## Conclusion

In this article, we learned about constant polynomials, their general form, graph, and degree. We also discussed the difference between constant polynomial and zero polynomial. Let’s solve a few examples and MCQs on constant polynomials for revision!

## Solved Examples of Constant Polynomials:

**1. Find the constant term in the polynomial **$P(x) = 3x^{2} + 7x + 9$**.**

**Solution:**

To find the constant term, we look for the term without any variable (term where the degree of x is 0).

In this case, the constant term is 9.

**2. Determine the degree of the polynomial P(x) = 4.**

**Solution:**

P(x) = 4

This is a constant polynomial.

We can express the polynomial in terms of x as

P(x) = 4x^{0}

So, the degree of the polynomial is 0.

**3. Find the value of the polynomial P(x) = 5.9 at x = 10.**

**Solution:**

P(x) = 5.9 is a constant polynomial.

So, for any value of x, the polynomial will give the same value, which is 5.9.

Thus, P(10) = 5.9

**4. Find the sum of two constant polynomials: P(x) = 4 and Q(x) =****-2****.**

**Solution:**

The sum of two constant polynomials is obtained by adding their constant values. It is a constant polynomial again.

In this case, P(x) + Q(x) = 4 + (** –** 2) = 2.

## Practice Problems on Constant Polynomials

## Constant Polynomial: Definition, Degree, Graph, Examples, FAQs

### What is the degree of a constant polynomial?

A constant polynomial has a degree of 0 because it does not involve any variable.

### Which of the following is an example of a constant polynomial?

The constant polynomial is -6.

### What is the graph of a constant polynomial?

The graph of a constant polynomial is a horizontal line parallel to the x-axis.

### The graph of zero polynomial is

The graph of zero polynomial is the x-axis itself.

## Frequently Asked Questions on Constant Polynomials

**What is the constant term in a polynomial? How to find the constant of a polynomial?**

The **constant of a polynomial** is the term that does not involve any variable. It is a fixed numerical value within the polynomial expression.

**Can the constant of a polynomial be 0?**

Yes, the constant term of a polynomial can be 0. For example, the constant term in the polynomial $x^{2} + 3x$ is 0.

**What is the polynomial of degree 1 called?**

A linear polynomial

**What are the polynomials with two terms called?**

Polynomials with two terms are called binomials.