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: 73

Answer

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

Work Step by Step

Factoring the $GCF= x^4 $, then the given expression, $ x^6+x^5y-2x^4y^2 $ is equivalent to \begin{array}{l} x^4(x^2+xy-2y^2) .\end{array} The two numbers whose product is $ac= 1(-2)=-2 $ and whose sum is $b= 1 $ are $\{ 2,-1 \}$. Using these two numbers to decompose the middle term of the expression, $ x^4(x^2+xy-2y^2) ,$ then the factored form is \begin{array}{l} x^4(x^2+2xy-1xy-2y^2) \\\\= x^4[(x^2+2xy)-(1xy+2y^2)] \\\\= x^4[x(x+2y)-y(x+2y)] \\\\= x^4[(x+2y)(x-y)] \\\\= x^4(x+2y)(x-y) .\end{array}
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