Question

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

Answer 1

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

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)`