How do you factor #6x^2-13x+6#?

1 Answer
Nov 19, 2015

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

Explanation:

#6x^2-13x+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 + c#, we need to think of 2 numbers such that:
#N_1*N_2 = a*c = 6*6 = 36#
AND
#N_1 +N_2 = b = -13#
After trying out a few numbers we get #N_1 = -9# and #N_2 =-4#
#-9*-4 = 36#, and #-9+(-4)= -13#

#6x^2-13x+6 = 6x^2-9x-4x+6#

# = 3x(2x-3) - 2(2x-3)#

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

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