Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 5 - Section 5.4 - Factoring Trinomials - Exercise Set - Page 362: 83

Answer

$(2x^2-3)(x^2+1)$.

Work Step by Step

The given expression is $=2x^4-x^2-3$. We can write $=2(x^2)^2-x^2-3$ Substitute $x^2=u$. $=2(u)^2-u-3$ Simplify. $=2u^2-u-3$ Rewrite $-u$ as $-3u+2u$. $=2u^2-3u+2u-3$ Factor. $=u(2u-3)+1(2u-3)$ $=(2u-3)(u+1)$. Substitute back $u=x^2$. $=(2x^2-3)(x^2+1)$.
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