Question

How do you factor `8x^3-8`?

Answer 1

`8x^3-8 = 8(x^3-1) = 8(x^3-1^3)`

`= 8(x-1)(x^2+x+1)`

Using the difference of cubes identity
`a^3-b^3 = (a-b)(a^2+ab+b^2)`

The quadratic factor can only be split into linear factors with complex coefficients.