Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set: 85

Answer

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

Work Step by Step

Factoring the $GCF=2xy$, then the given expression, $ 2x^3y+2x^2y-12xy $, is equivalent to \begin{array}{l} 2xy(x^2+x-6) .\end{array} The two numbers whose product is $ac= 1(-6)=-6 $ and whose sum is $b= 1 $ are $\{ 3,-2 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 2xy(x^2+x-6) $, is \begin{array}{l}\require{cancel} 2xy(x^2+3x-2x-6) \\\\= 2xy[(x^2+3x)-(2x+6)] \\\\= 2xy[x(x+3)-2(x+3)] \\\\= 2xy[(x+3)(x-2)] \\\\= 2xy(x+3)(x-2) .\end{array}
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