Question

# Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary: 10x^{2}-160

Polynomial factorization
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary:
$$10x^{2}-160$$

## Expert Answers (1)

2021-06-08

Step 1
We have to factorize the polynomial:
$$10x^{2}-160$$
Taking 10 common from the polynomial, we get
$$10x^{2}-160=10(x^{2}-16)$$
$$=10(x^{2}-4^{2})$$
Step 2
We know the algebraic identity,
$$a^{2}-b^{2}=(a-b)(a+b)$$
Applying above identity for $$x^{2}-4^{2}$$, we get
$$10(x^{2}-4^{2})=10(x-4)(x+4)$$
Hence, factorize form of polynomial is $$10(x−4)(x+4).$$