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: 46

Answer

$-2(x-24)(x+3)$

Work Step by Step

Factoring the negative $GCF= -2 $, the given expression, $ -2x^2+42x+144 ,$ is equivalent to \begin{array}{l} -2(x^2-21x-72) .\end{array} The 2 numbers whose product is $ac= 1(-72)=-72 $ and whose sum is $b= -21 $ are $\left\{ -24,3 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} -2(x^2-24x+3x-72) \\\\= -2[(x^2-24x)+(3x-72)] \\\\= -2[x(x-24)+3(x-24)] \\\\= -2[(x-24)(x+3)] \\\\= -2(x-24)(x+3) .\end{array}
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