Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Appendix A - Review - A.3 Polynomials - A.3 Assess Your Understanding - Page A30: 112

Answer

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

Work Step by Step

Let $x^2=a$. $4-14x^2-8x^4=4-14a-8a^2$ Factor out $2$. $=2(2-7a-4a^2)$ Rewrite $-7a$ as $-8a+1a$ $=2(2-8a+1a-4a^2)$ Group the first two terms together and group the last two terms together. $=2[(2-8a)+(1a-4a^2)]$ Factor out the GCF in each group. $=2[2(1-4a)+a(1-4a)]$ Factor out $(1-4a)$. $=2(1-4a)(2+a)$ Back substitute $a=x^2$. $=2(1-4x^2)(2+x^2)$ $=2[1^2-(2x)^2](2+x^2)$ Use special formula $a^2-b^2=(a+b)(a-b)$ wehere $a=1$ and $b=2x$. $=2(1+2x)(1-2x)(2+x^2)$ $=2(2x+1)[-(-1+2x)](x^2+2)$ $=-2(2x+1)(2x-1)(x^2+2)$ Hence, the completely factored form of the given expression is $-2(2x+1)(2x-1)(x^2+2)$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.