# How do you determine the binomial factors of #x^3-2x^2-4x+8#?

##### 1 Answer

Mar 3, 2018

#### Explanation:

Given:

#x^3-2x^2-4x+8#

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

So this quadrinomial will factor by grouping:

#x^3-2x^2-4x+8 = (x^3-2x^2)-(4x-8)#

#color(white)(x^3-2x^2-4x+8) = x^2(x-2)-4(x-2)#

#color(white)(x^3-2x^2-4x+8) = (x^2-4)(x-2)#

#color(white)(x^3-2x^2-4x+8) = (x^2-2^2)(x-2)#

#color(white)(x^3-2x^2-4x+8) = (x-2)(x+2)(x-2)#

#color(white)(x^3-2x^2-4x+8) = (x-2)^2(x+2)#