Question

How do I factor `x^3-2x^2-4x+8` completely?

Answer 1

Factor `x^3 - 2x^2 - 4x + 8`

Ans: `(x - 2)^2(x + 2)`

Explanation:

Factor by grouping:

`x^2(x - 2) - 4(x - 2) = (x - 2)(x^2 - 4) =`

`= (x - 2)^2(x + 2)`

Answer 2

Factor by grouping first, then use the formula for the difference of two squares.

Explanation:

Your expression looks like this

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

You can factor this expression by grouping the first and third terms

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

This is equivalent to

`x(x^2 - 4) - 2(x^2 - 4) = (x^2 - 4)(x-2)`

The first binomial is actually the difference of two perfect squares, which means that you can write it as

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

Your expression will thus be

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