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, $6x^2 + 11x + 3$ = $(2x + 3)(3x + 1)$
