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: 36

Answer

$2(a-7)(a+5)$

Work Step by Step

Factoring the $GCF= 2 $, the given expression, $ 2a^2-4a-70 ,$ is equivalent to \begin{array}{l} 2(a^2-2a-35) .\end{array} The 2 numbers whose product is $ac= 1(-35)=-35 $ and whose sum is $b= -2 $ are $\left\{ -7,5 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} 2(a^2-7a+5a-35) \\\\= 2[(a^2-7a)+(5a-35)] \\\\= 2[a(a-7)+5(a-7)] \\\\= 2[(a-7)(a+5)] \\\\= 2(a-7)(a+5) .\end{array}
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