Question

How do you factor `(x^3)- 100 = 0`?

Answer 1

`(x-root 3 100)(x^2+xroot3 100+ (root 3 100)^2)=0`

Explanation:

We could use the fact that `a^3-b^3=(a-b)(a^2+ab+b^2)`

So we could rewrite `x^3-100=0` as
`x^3-(root 3 100)^3=0=>(x-root 3 100)(x^2+xroot3 100+ (root 3 100)^2)=0`

To find the values of `x`, you could solve the following equations:
`x-root 3 100=0` and `x^2+xroot3 100+ (root 3 100)^2=0`.