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: 29


$ (5z-3)(5z-3) $

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 --- $25z^{2}-30z+9 =...$ Always start by searching for a GCF ... (there are none other than 1). 1. $\quad ac=225\qquad (25\times 9=5\times 5\times 3\times 3)$ 2. $\quad$sum = $-30 \quad$... factors: $-15$ and $-15$ 3. $\quad 25z^{2}-30z+9 =(25z^{2}-15z)+(-15z+9)$ 4. $\quad$... $=5z(5z-3) +(-3)(5z-3) = (5z-3)(5z-3)$ Check by FOIL $F:\quad 25z^{2}$ $O:\quad -15z$ $I:\quad -15z$ $L:\quad +9$ $ (5z-3)(5z-3) $ = $25z^{2}-30z+9$
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