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: 30


$ (3z+2)(3z+2) $

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 --- $9z^{2}+12z+4 =...$ Always start by searching for a GCF ... (there are none other than 1). 1. $\quad ac=36\qquad $ 2. $\quad$sum = $+12 \quad$... factors: $+6$ and $+6$ 3. $\quad 9z^{2}+12z+4 =(9z^{2}+6z)+(6z+4)$ 4. $\quad$... $=3z(3z+2) +(2)(3z+2) = (3z+2)(3z+2)$ Check by FOIL $F:\quad 9z^{2}$ $O:\quad +6z$ $I:\quad +6z$ $L:\quad +4$ $ (3z+2)(3z+2) $ = $9z^{2}+12z+4$
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