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: 1


$ (2x+3)(x+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. $ac=6$ 2. sum = 5... factors: 2 and 3 3. $2x^{2}+5x+3=(2x^{2}+2x)+(3x+3)$ 4. ... $=2x(x+1)+3(x+3)$ $=(2x+3)(x+1)$ Check by FOIL$\qquad (2x+3)(x+1) $= $F:\quad 2x^{2}$ $O:\quad +2x$ $I:\quad +3x$ $L:\quad +3$ $ (2x+3)(x+1) $= $2x^{2}+5x+3$
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