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 - Page 303: 52



Work Step by Step

The two numbers whose product is $ac= 12(6)=72 $ and whose sum is $b= -17 $ are $\{ -8,-9 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 12x^2-17x+6 $, is \begin{array}{l}\require{cancel} 12x^2-8x-9x+6 \\\\= (12x^2-8x)-(9x-6) \\\\= 4x(3x-2)-3(3x-2) \\\\= (3x-2)(4x-3) .\end{array}
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