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: 60



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 --- $4x^{2}-18x-10 =...$ Always start by searching for a GCF ... ($GCF=2$). $=2(2x^{2}-9x-5)=...$ Now, the parentheses: 1. $\quad ac=-10 \qquad $ 2. $\quad$sum = $-9\quad$... factors: $-10$ and $+1$ 3. $\quad$ $2x^{2}-9x-5 = (2x^{2}-10\mathrm{x})+(x-5)$ 4. $\quad$... $= 2x(x-5)+(1)(x-1) = (2x+1)(x-5) $ $...=2(2x^{2}+13x+15) = 2(2x+1)(x-5)$
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