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 443: 20


$(2w-3)(3w-4) $

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. $\quad ac=+72$ 2. $\quad$sum = $-17 \quad$... factors: $-8$ and $-9$ 3. $\quad$ $6w^{2}-17w+12=(6w^{2}-9w)+(-8w+12)$ 4. $\quad$... $=3w(2w-3) +(-4)(2w-3) =(2w-3)(3w-4)$ Check by FOIL $F:\quad 6w^{2}$ $O:\quad -8w$ $I:\quad -9w$ $L:\quad +12$ $(2w-3)(3w-4) $ = $6w^{2}-17w+12$
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