Intermediate Algebra (6th Edition)

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

Chapter 5 - Section 5.7 - Factoring by Special Products - Exercise Set: 8

Answer

$2(x+7)^2$

Work Step by Step

Factoring the $GCF=2$, then the given expression, $ 2x^2+28x+98 $, is equivalent to \begin{array}{l} 2(x^2+14x+49) .\end{array} The two numbers whose product is $ac= 1(49)=49 $ and whose sum is $b= 14 $ are $\{ 7,7 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 2(x^2+14x+49) $, is \begin{array}{l}\require{cancel} 2(x^2+7x+7x+49) \\\\= 2[(x^2+7x)+(7x+49)] \\\\= 2[x(x+7)+7(x+7)] \\\\= 2[(x+7)(x+7)] \\\\= 2(x+7)^2 .\end{array}
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