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: 5


$ (x+4)(2x+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 --- Always start by searching for a GCF.... none (other than 1). 1. $ac=24$ 2. sum = $11$... factors: $3$ and $8$ 3. $2x^{2}+11x+12=(2x^{2}+ 8x)+(3x+12)$ 4. ... $=2x(x+1)+3( x+4)$ $=(x+4)(2x+3)$ Check by FOIL$\qquad (x+4)(2x+3) $= $F:\quad 2x^{2}$ $O:\quad +3x$ $I:\quad +8x$ $L:\quad +12$ $ (x+4)(2x+3) $= $2x^{2}+11x+12$
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