Answer
Chapter 6 - Section 6.4 - Exercise Set: 11 (Answer)
Factorize : $15x^2 - 23x + 4$
a) The two numbers are -3 and -20.
b) -23x to be re-written as -20x - 3x
c) $15x^2 - 23x + 4$ = $(3x - 4)(5x - 1)$
Work Step by Step
Chapter 6 - Section 6.4 - Exercise Set: 11 (Solution)
Factorize : $15x^2 - 23x + 4$
First, to look for two numbers whose product is +60 and whose sum is -23. As the two numbers have a positive product and a negative sum, pairs of negative factors of 60 are to be investigated only.
Factors of 60 $\Longleftrightarrow$ Sum of Factors
-1,-60 $\Longleftrightarrow$ -61 (Incorrect sum)
-2,-30 $\Longleftrightarrow$ -32 (Incorrect sum)
-3,-20 $\Longleftrightarrow$ -23 (Correct sum)
a) The two numbers are -3 and -20.
b) -23x to be re-written as -20x - 3x
c) $15x^2 - 23x + 4$
= $(15x^2 - 20x - 3x + 4)$ (from the two correct numbers worked out)
= $(15x^2 - 20x) - (3x - 4)$ (Group the terms)
= $5x(3x - 4) - (3x - 4)$ (Factor each group)
= $(3x - 4)(5x - 1)$ (Factor out (3x - 4))
Thus, $15x^2 - 23x + 4$ = $(3x - 4)(5x - 1)$
