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: 62



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 --- $12x^{2}-33x+21 =...$ Always start by searching for a GCF ... ($GCF=3$). $=3(4x^{2}-11x+7)=...$ Now, the parentheses: 1. $\quad ac=28 \qquad $ 2. $\quad$sum = $-11\quad$... factors: $-7$ and $-4$ 3. $\quad (4x^{2}-11x+7) = (4x^{2}-4x)+(-7x+7)$ 4. $\quad$... $= 4x(x-1)+(-7)(x-1) = (4x-7)(x-1) $ $...$= $3(4x-7)(x-1)$
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