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 - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set: 44

Answer

$2x(x-12)(x-8)$

Work Step by Step

Factoring the $GCF= 2x $, the given expression, $ 2x^3-40x^2+192x ,$ is equivalent to \begin{array}{l} 2x(x^2-20x+96) .\end{array} The 2 numbers whose product is $ac= 1(96)=96 $ and whose sum is $b= -20 $ are $\left\{ -12,-8 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} 2x(x^2-12x-8x+96) \\\\= 2x[(x^2-12x)-(8x-96)] \\\\= 2x[x(x-12)-8(x-12)] \\\\= 2x[(x-12)(x-8)] \\\\= 2x(x-12)(x-8) .\end{array}
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