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: 18



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. $\quad ac=-84$ 2. $\quad$sum = $-25 \quad$... factors: $-28$ and $+3$ 3. $\quad 3x^{2}-25x-28=(3x^{2}+3x)+(-28x-28)$ 4. $\quad$... $=3x(x+1) +(-28)(x+1) =(x+1)(3x-28)$ Check by FOIL $F:\quad 3x^{2}$ $O:\quad -28x$ $I:\quad +3x$ $L:\quad -28$ $(x+1)(3x-28)$ = $3x^{2}-25x-28$
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