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: 19


$(3w-4)(2w-1) $

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. $\quad ac=+24$ 2. $\quad$sum = $-11 \quad$... factors: $-8$ and $-3$ 3. $\quad$ $6w^{2}-11w+4=(6w^{2}-8w)+(-3w+4)$ 4. $\quad$... $=2w(3w-4) +(-1)(3w-4) =(3w-4)(2w-1)$ Check by FOIL $F:\quad 6w^{2}$ $O:\quad -3w$ $I:\quad -8w$ $L:\quad +4$ $(3w-4)(2w-1) $ = $6w^{2}-11w+4$
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