How to decompose $x^3-1$ I need to decompose $x^3-1$, I know the Binomial theorem, and finding roots of a polynomial, how should I approach this? 

We can just use binomial theorem:
Observe
$$(x-1)^3=x^3-3x^2+3x-1$$
So $$\begin{align}x^3-1&=(x-1)^3+3x^2-3x\\
&=(x-1)^3+3x(x-1)\\
&=(x-1)((x-1)^2+3x)\\
&=(x-1)(x^2+x+1)\end{align}$$
Hope this helps.
P.S.
If factoring $x^2+x+1$ is needed, recall we have a formula for quadratic polynomials.
