Question

How do you factor `x^4-8x`?

Answer 1

In this way:

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

The last passage is because `(x^3-8)` is a difference of two cubes, that can be factored with this rule:

`a^3-b^3=(a-b)(a^2+ab+b^2)`.

The last quadratic polynomial can't be further factored.