How do you factor 6x^2-13x+66x2−13x+6?

1 Answer
Don't Memorise
Nov 19, 2015

6x^2-13x+6=color(green)((2x-3)(3x-2)6x2−13x+6=(2x−3)(3x−2)

Explanation:

6x^2-13x+66x2−13x+6

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like ax^2 + bx + cax2+bx+c, we need to think of 2 numbers such that:
N_1*N_2 = a*c = 6*6 = 36N1⋅N2=a⋅c=6⋅6=36
AND
N_1 +N_2 = b = -13N1+N2=b=−13
After trying out a few numbers we get N_1 = -9N1=−9 and N_2 =-4N2=−4
-9*-4 = 36−9⋅−4=36, and -9+(-4)= -13−9+(−4)=−13

6x^2-13x+6 = 6x^2-9x-4x+66x2−13x+6=6x2−9x−4x+6

= 3x(2x-3) - 2(2x-3)=3x(2x−3)−2(2x−3)

(2x-3)(2x−3) is a common factor to each of the terms

=color(green)((2x-3)(3x-2)=(2x−3)(3x−2)

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