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: 60

Answer

$a^3(a-5b)(a+b)$

Work Step by Step

Factoring the $GCF= a^3 $, then the given expression, $ a^5-4a^4b-5a^3b^2 $ is equivalent to \begin{array}{l} a^3(a^2-4ab-5b^2) .\end{array} The two numbers whose product is $ac= 1(-5)=-5 $ and whose sum is $b= -4 $ are $\{ -5,1 \}$. Using these two numbers to decompose the middle term of the expression, $ a^3(a^2-4ab-5b^2) ,$ then the factored form is \begin{array}{l} a^3(a^2-5ab+ab-5b^2) \\\\= a^3[(a^2-5ab)+(ab-5b^2)] \\\\= a^3[a(a-5b)+b(a-5b)] \\\\= a^3[(a-5b)(a+b)] \\\\= a^3(a-5b)(a+b) .\end{array}
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