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: 33

Answer

$(x+9)(2x-3)$

Work Step by Step

The two numbers whose product is $ac= 2(-27)=-54 $ and whose sum is $b= 15 $ are $\{ 18,-3 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 2x^2+15x-27 $, is \begin{array}{l}\require{cancel} 2x^2+18x-3x-27 \\\\= (2x^2+18x)-(3x+27) \\\\= 2x(x+9)-3(x+9) \\\\= (x+9)(2x-3) .\end{array}
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