Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set: 97

Answer

$-x(x^2+9)(x^2-2)$

Work Step by Step

Factoring the $GCF= x ,$ the given expression is equivalent to \begin{array}{l}\require{cancel} -(x^5+7x^3-18x) \\\\= -x(x^4+7x^2-18) .\end{array} Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{ expression }$ \begin{array}{l}\require{cancel} (x^4+7x^2-18) \end{array} has $c= -18 $ and $b= 7 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ 9,-2 \right\}.$ Using these two numbers, the $\text{ expression }$ above is equivalent to \begin{array}{l}\require{cancel} -x(x^2+9)(x^2-2) .\end{array}
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