Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 6 - Section 6.4 - Factoring Trinomials of the Form ax2+bx+c by Grouping - Exercise Set: 9

Answer

Chapter 6 - Section 6.4 - Exercise Set: 9 (Answer) Factorize : $6x^2 + 11x + 3$ a) The two numbers are 2 and 9. b) 11x to be re-written as 9x + 2x c) $6x^2 + 11x + 3$ = $(2x + 3)(3x + 1)$

Work Step by Step

Chapter 6 - Section 6.4 - Exercise Set: 9 (Solution) Factorize : $6x^2 + 11x + 3$ First, to look for two numbers whose product is +18 and whose sum is +11. As the two numbers have a positive product and a positive sum, pairs of positive factors of 18 are to be investigated only. Factors of 18 $\Longleftrightarrow$ Sum of Factors 1,18 $\Longleftrightarrow$ 19 (Incorrect sum) 2,9 $\Longleftrightarrow$ 11 (Correct sum) a) The two numbers are 2 and 9. b) 11x to be re-written as 9x + 2x c) $6x^2 + 11x + 3$ = $(6x^2 + 9x + 2x + 3)$ (from the two correct numbers worked out) = $(6x^2 + 9x) + (2x + 3)$ (Group the terms) = $3x(2x + 3) + (2x + 3)$ (Factor each group) = $(2x + 3)(3x + 1)$ (Factor out (2x + 3)) Thus, $6x^2 + 11x + 3$ = $(2x + 3)(3x + 1)$
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