How do you factor #3x^3 - 2[ x - ( 3 - 2x ) ] = 3 ( x - 2 )^2#?

1 Answer
Jan 27, 2018

Answer:

The factored form is #3(x^2+2)(x-1)=0#.

Explanation:

#3x^3-2[color(blue)(x-(3-2x))]=3color(red)((x-2)^2)#

#3x^3-2[color(blue)(x-3+2x)]=3color(red)((x^2-4x+4))#

#3x^3-2[color(blue)(3x-3)]=color(red)(3x^2-12x+12)#

#3x^3-color(blue)(6x+6)=color(red)(3x^2-12x+12)#

#3x^3-3x^2+6x-6=0#

#3x^2(x-1)+6(x-1)=0#

#(3x^2+6)(x-1)=0#

#3(x^2+2)(x-1)=0#