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: 3


$ (x+4)(3x+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 = $13$... factors: $1$ and $12$ 3. $3x^{2}+13x+4=(3x^{2}+ x)+(12x+4)$ 4. ... $=x(3x+1)+4(3x+1)$ $=(x+4)(3x+1)$ Check by FOIL$\qquad (x+4)(3x+1) $= $F:\quad 3x^{2}$ $O:\quad +x$ $I:\quad +12x$ $L:\quad +4$ $ (x+4)(3x+1) $= $3x^{2}+13x+4$
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