Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.4 - Factoring Trinomials of the Form ax^2+bx+c - Problem Set 6.4: 7

Answer

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

Work Step by Step

In accordance with the rules of factoring trinomials, we need to find two integers whose product is $240$ and whose sum is $-31$. A little searching determines that these numbers are $-15$ and $-16$. Therefore, we can express the middle term $-31x$ as $(-15x-16x)$ and proceed to factoring by grouping: $12x^{2}-31x+20$ =$12x^{2}-15x-16x+20$ =$3x(4x-5)-4(4x-5)$ =$(4x-5)(3x-4)$
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