How do you factor #4x^3+2x^2-2x-1#?

1 Answer
Sep 1, 2016

Answer:

#4x^3+2x^2-2x-1=(sqrt(2)x-1)(sqrt(2)x+1)(2x+1)#

Explanation:

Notice that the ratio of the first and second terms is the same as that of the third and fourth terms. So this cubic will factor by grouping:

#4x^3+2x^2-2x-1#

#=(4x^3+2x^2)-(2x+1)#

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

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

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

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