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: 21


$ (x+4)(8x+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. $\quad ac=+32$ 2. $\quad$sum = $+33 \quad$... factors: $+32$ and $+1$ 3. $\quad 8x^{2}+33x+4=(8x^{2}+32x)+( x+4)$ 4. $\quad$... $=8x(x+4) +(1)(x+4) =(x+4)(8x+1)$ Check by FOIL $F:\quad 8x^{2}$ $O:\quad +x$ $I:\quad +32x$ $L:\quad +4$ $ (x+4)(8x+1) $ = $8x^{2}+33x+4$
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