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.