How do you factor #x^3+2x^2-8x-16#?

1 Answer
Aug 28, 2016

Answer:

#x^3+2x^2-8x-16=(x-2sqrt(2))(x+2sqrt(2))(x+2)#

Explanation:

Given:

#x^3+2x^2-8x-16#

Notice that the ratio between the first and second terms is the same as that between the third and fourth terms.

So this cubic will factor by grouping:

#x^3+2x^2-8x-16#

#=(x^3+2x^2)-(8x+16)#

#=x^2(x+2)-8(x+2)#

#=(x^2-8)(x+2)#

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

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