## Intermediate Algebra for College Students (7th Edition)

Published by Pearson

# Chapter 5 - Section 5.5 - Factoring Special Forms - Exercise Set - Page 372: 101

#### Answer

$(x^4+1)(x+2)(x-2)(x^2+4)$

#### Work Step by Step

The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$. Hence here: $x^8-15x^4-16=\\=x^8+x^4-16x^4-16\\=x^4(x^4+1)-16(x^4+1)\\=(x^4+1)(x^4-16)\\=(x^4+1)((x^2)^2-4^2)\\=(x^4+1)(x^2-4)(x^2+4)\\=(x^4+1)(x^2-2^2)(x^2+4)\\=(x^4+1)(x+2)(x-2)(x^2+4)$

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