## Algebra: A Combined Approach (4th Edition)

Chapter 6 - Section 6.4 - Exercise Set: 10 (Answer) Factorize : $8x^2 + 14x + 3$ a) The two numbers are 2 and 12. b) 14x to be re-written as 12x + 2x c) $8x^2 + 14x + 3$ = $(2x + 3)(4x + 1)$
Chapter 6 - Section 6.4 - Exercise Set: 10 (Solution) Factorize : $8x^2 + 14x + 3$ First, to look for two numbers whose product is +24 and whose sum is +14. As the two numbers have a positive product and a positive sum, pairs of positive factors of 24 are to be investigated only. Factors of 24 $\Longleftrightarrow$ Sum of Factors 1,24 $\Longleftrightarrow$ 25 (Incorrect sum) 2,12 $\Longleftrightarrow$ 14 (Correct sum) a) The two numbers are 2 and 12. b) 14x to be re-written as 12x + 2x c) $8x^2 + 14x + 3$ = $(8x^2 + 12x + 2x + 3)$ (from the two correct numbers worked out) = $(8x^2 + 12x) + (2x + 3)$ (Group the terms) = $4x(2x + 3) + (2x + 3)$ (Factor each group) = $(2x + 3)(4x + 1)$ (Factor out (2x + 3)) Thus, $8x^2 + 14x + 3$ = $(2x + 3)(4x + 1)$