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: 51

Answer

$(4x-3)(2x-5)$

Work Step by Step

The two numbers whose product is $ac= 8(15)=120 $ and whose sum is $b= -26 $ are $\{ -6,-20 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 8x^2-26x+15 $, is \begin{array}{l}\require{cancel} 8x^2-6x-20x+15 \\\\= (8x^2-6x)-(20x-15) \\\\= 2x(4x-3)-5(4x-3) \\\\= (4x-3)(2x-5) .\end{array}
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