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: 18

Answer

$4x(x-2)(5x+9)$

Work Step by Step

Factoring the $GCF= 4x $, then the given expression, $ 20x^3-4x^2-72x $ is equivalent to \begin{array}{l} 4x(5x^2-x-18) .\end{array} The two numbers whose product is $ac= 5(-18)=-90 $ and whose sum is $b= -1 $ are $\{ -10,9 \}$. Using these two numbers to decompose the middle term of the trinomial above, then the complete factored form is \begin{array}{l} 4x(5x^2-10x+9x-18) \\\\= 4x[(5x^2-10x)+(9x-18)] \\\\= 4x[5x(x-2)+9(x-2)] \\\\= 4x[(x-2)(5x+9)] \\\\= 4x(x-2)(5x+9) .\end{array}
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