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: 20

Answer

$4(x+9)(x-4)$

Work Step by Step

Factoring the $GCF= 4 $, then the given expression, $ 4x^2+20x-144 $ is equivalent to \begin{array}{l} 4(x^2+5x-36) .\end{array} The two numbers whose product is $ac= 1(-36)=-36 $ and whose sum is $b= 5 $ are $\{ 9,-4 \}$. Using these two numbers to decompose the middle term of the trinomial above, then the complete factored form is \begin{array}{l} 4(x^2+9x-4x-36) \\\\= 4[(x^2+9x)-(4x+36)] \\\\= 4[x(x+9)-4(x+9)] \\\\= 4[(x+9)(x-4)] \\\\= 4(x+9)(x-4) .\end{array}
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