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: 12



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.... none (other than 1). 1. $ac=-15$ 2. sum = $+14$ ... factors: $-1$ and $+15$ 3. $3x^{2}+14x-5=(3x^{2}+15x)+(-x-5)$ 4. ... $=3x(x+5)+(-1)(x+5)$ $=(3x-1)(x+5)$ Check by FOIL$\qquad (3x-1)(x+5) $= $F:\quad 3x^{2}$ $O:\quad +15x$ $I:\quad -x$ $L:\quad -5$ $(3x-1)(x+5)$ = $3x^{2}+14x-5$
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