Table of Contents

**Class 7 algebraic expression | Factorization of Polynomials**

**Table of Contents**

- Factorization of Polynomials
- Zero of a polynomial
- Summary
- What’s Next?

In the previous segment, we learnt how to find the **factors of a number**. In this segment, we will learn about the factorization of a polynomial.

## How do we find the factors of a polynomial?

If a polynomial can be written as a product of two polynomials, then these polynomials are known as the factors of the original polynomial.

Each factor of a polynomial shows the following characteristics:

- The degree will be less than the degree of the polynomial.
- It cannot be factorized further.

For example, Consider ?^{2} + 3? + 2.

?^{2} + 3? + 2 = (x+1)(x+2)

Thus, (x+1) and (x+2) are the factors of (?^{2} + 3? + 2

- (x+1) and (x+2) have degree 1, which is less than that of the polynomial which has degree 2.
- (x + 1) and (x+2) are in the simplest form and cannot be factorised further.

## What are Zeroes of a polynomial?

- Zero of a polynomial is a number when substituted in place of the variable gives the value of the polynomial equal to zero.
- In some cases, factorization helps to get the zeroes of the polynomial.

For example,

(x+1) and (x+2) are the factors of ?^{2} + 3? + 2

The opposite of the numbers +1 and +2 are -1 and -2 respectively. Thus, the zeroes of the polynomial ?^{2} + 3? + 2 are -1 and -2.

These two numbers are called the zeroes of the polynomial. Substituting either of these values in ?^{2} + 3? + 2 will give zero.