<s>[INST] 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? 
 [/INST] You have $(x-1)(x^2+x+1)$ now we need a root for the second polynomial.
We have $x^2+x+1=0\iff x^2+x+\frac{1}{4}=\frac{-3}{4}\iff(x+\frac{1}{2})^2=\frac{-3}{4}\iff x+\frac{1}{2}=\frac{\pm\sqrt{-3}}{2}$
$\iff x=\frac{\pm\sqrt{-3}-1}{2}$
So the polynomial is equal to:
$(x-1)(x+\frac{1+\sqrt{3}i}{2})(x+\frac{1-\sqrt{3}i}{2})$
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