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: 10


$(3y-4)(y+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.... none (other than 1). 1. $ac=-12$ 2. sum = $-1$ ... factors: $-4$ and $+3$ 3. $3y^{2}-y-4=(3y^{2}+3y)+(-4y-4)$ 4. ... $=3y(y+1)+(-4)(y+1)$ $=(3y-4)(y+1)$ Check by FOIL$\qquad (3y-4)(y+1) $= $F:\quad 3y^{2}$ $O:\quad +3y$ $I:\quad -4y$ $L:\quad -4$ $(3y-4)(y+1) $= $3y^{2}-y-4$
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