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
ANSWERED
asked 2021-06-07
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 \(10(x−4)(x+4).\)

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