Factor the polynomial completely by first factoring out the GFC and then by regrouping #12x^2y-18xy+4x-6#?

1 Answer
Jan 26, 2018

#2(2x-3)(3xy+1)#

Explanation:

#12x^2y - 18xy + 4x - 6#

GCF of #12, 18, 4, 6 = 2#

#12x^2y - 18xy + 4x - 6 = 2 (6x^2y - 9xy + 2x - 3)#

#6/2 = 9/3 = 3#

this means that when #6x^2y# is grouped with #2x#, and #-9xy# is grouped with #-3#, the common factor between them can be the same.

regrouping accordingly:

#6x^2y - 9xy + 2x - 3 = 6x^2y + 2x - 9xy - 3#

#6x^2y + 2x = 2x(3xy + 1)#

#-9xy - 3 = -3(3xy + 1)#

#6x^2y - 9xy + 2x - 3x = 2x(3xy+ 1) -3(3xy + 1)#

#2x(3xy+1) - 3(3xy+1) = (2x-3)(3xy+1)#

#12x^2y - 18xy + 4x - 6 = 2(2x-3)(3xy+1)#