How do you factor #4x^3 + 2x^2 - 24x - 12#?

1 Answer
May 22, 2016

Answer:

#4x^3+2x^2-24x-12#

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

#=2(x-sqrt(6))(x+sqrt(6))(2x+1)#

Explanation:

Notice that the ratio of the coefficients of the first and second terms is the same as the ratio of the coefficients of the third and fourth terms, so this cubic can be factored by grouping:

#4x^3+2x^2-24x-12#

#=(4x^3+2x^2)-(24x+12)#

#=2x^2(2x+1)-12(2x+1)#

#=(2x^2-12)(2x+1)#

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

#=2(x-sqrt(6))(x+sqrt(6))(2x+1)#