Answer
Chapter 6 - Section 6.4 - Exercise Set: 12 (Answer)
Factorize : $6x^2 - 13x + 5$
a) The two numbers are -3 and -10.
b) -13x to be re-written as -3x - 10x
c) $6x^2 - 13x + 5$ = $(2x - 1)(3x - 5)$
Work Step by Step
Chapter 6 - Section 6.4 - Exercise Set: 12 (Solution)
Factorize : $6x^2 - 13x + 5$
First, to look for two numbers whose product is +30 and whose sum is -13. As the two numbers have a positive product and a negative sum, pairs of negative factors of 30 are to be investigated only.
Factors of 30 $\Longleftrightarrow$ Sum of Factors
-1,-30 $\Longleftrightarrow$ -31 (Incorrect sum)
-2,-15 $\Longleftrightarrow$ -17 (Incorrect sum)
-3,-10 $\Longleftrightarrow$ -13 (Correct sum)
a) The two numbers are -3 and -10.
b) -13x to be re-written as -3x - 10x
c) $6x^2 - 13x + 5$
= $(6x^2 - 3x - 10x + 5)$ (from the two correct numbers worked out)
= $(6x^2 - 3x) - (10x - 5)$ (Group the terms)
= $3x(2x - 1) - 5(2x - 1)$ (Factor each group)
= $(2x - 1)(3x - 5)$ (Factor out (2x - 1))
Thus, $6x^2 - 13x + 5$ = $(2x - 1)(3x - 5)$
