Factor #36x^3+12x^2-72x-24# ?

1 Answer
Dec 21, 2016

Answer:

#36x^3+12x^2-72x-24 = 12(x-sqrt(2))(x+sqrt(2))(3x+1)#

Explanation:

Note that the ratio of the #1#st and #2#nd terms is the same as that between the #3#rd and #4#th terms. So this cubic will factor by grouping. Also note that all of the coefficients are divisible by #12#, so we can separate that out as a factor first:

#36x^3+12x^2-72x-24 = 12(3x^3+x^2-6x-2)#

#color(white)(36x^3+12x^2-72x-24) = 12((3x^3+x^2)-(6x+2))#

#color(white)(36x^3+12x^2-72x-24) = 12(x^2(3x+1)-2(3x+1))#

#color(white)(36x^3+12x^2-72x-24) = 12(x^2-2)(3x+1)#

#color(white)(36x^3+12x^2-72x-24) = 12(x^2-(sqrt(2))^2)(3x+1)#

#color(white)(36x^3+12x^2-72x-24) = 12(x-sqrt(2))(x+sqrt(2))(3x+1)#