Answer
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) $8x^2 + 14x + 3$ = $(2x + 3)(4x + 1)$
Work Step by Step
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, $8x^2 + 14x + 3$ = $(2x + 3)(4x + 1)$
