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: 22


$ (x+6)(7x+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. $\quad ac=+42$ 2. $\quad$sum = $+43 \quad$... factors: $+42$ and $+1$ 3. $\quad 7x^{2}+43x+6=(7x^{2}+42x)+( x+6)$ 4. $\quad$... $=7x(x+6) +(1)(x+6) =(x+6)(7x+1)$ Check by FOIL $F:\quad 7x^{2}$ $O:\quad +x$ $I:\quad +42x$ $L:\quad +6$ $ (x+6)(7x+1) $ = $7x^{2}+43x+6$
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