College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.5 - Page 74: 69



Work Step by Step

We are given the expression $2x^{4}-162$. First, we can use the distributive property to factor out 2, the greatest common factor of both terms. $2x^{4}-162=2(x^{4}-81)$ If $a$ and $b$ are real numbers, we know that $a^{2}-b^{2}=(a+b)(a-b)$ Therefore, $2(x^{4}-81)=2(x^{2}+9)(x^{2}-9)$. In this case, $a=x^{2}$ and $b=9$.
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