Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Section 6.3 - Factoring Trinomials Whose Leading Coefficient is Not 1 - Exercise Set - Page 444: 26


$(2y-3)(3y+8) $

Work Step by Step

Factoring by grouping: 1. Multiply the leading coefficient, a, and the constant, c. 2. Find the factors of ac whose sum is b. 3. Rewrite the middle term, bx, as a sum or difference using the factors from step 2. 4. Factor by grouping --- Always start by searching for a GCF ... (there are none other than 1). 1. $\quad ac=-132\qquad (6\times 24=2\times 3\times 3\times 8)$ 2. $\quad$sum = $+7 \quad$... factors: $+16$ and $-9$ 3. $\quad 6y^{2}+7y-24 =(6y^{2}-9y)+(16y-24)$ 4. $\quad$... $=3y(2y-3)+(8)(2y-3) =(2y-3)(3y+8)$ Check by FOIL $F:\quad 6y^{2}$ $O:\quad +16y$ $I:\quad -9y$ $L:\quad -24$ $(2y-3)(3y+8) $ = $6y^{2}+7y-24$
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