Factorization of a polynomials in complex number. Factorize this expression:
$$a^2+b^2+c^2-ab-bc-ca.$$
The result is 
$$(a+b\Omega+c\Omega^2)(a+b\Omega^2+c\Omega)$$
How I can get $\Omega$ here?What's the approach?

we have
$$(a+b\Omega+c\Omega^2)(a+b\Omega^2+c\Omega)$$$$=a^2+ab\Omega^2+ac\Omega+ab\Omega+b^2\Omega^3+bc\Omega^2+ac\Omega^2+bc\Omega^4+c^2\Omega^3$$
$$=a^2+\Omega^3b^2+\Omega^3c^2+(\Omega^2+\Omega)ab+(\Omega^2+\Omega^4)bc+(\Omega+\Omega^2)ac$$
$$=a^2+b^2+c^2-ab-bc-ac$$
It follows that $$\Omega^3=1$$
and
$$\Omega^2+\Omega=\Omega^2+\Omega^4=-1.$$
Solving $$\Omega^2+\Omega=-1$$ will give you two solutions that work (check that they satisfy all of the above equations).  These happen to be the primitive third roots of unity as $$\Omega^2+\Omega+1$$ is the third cyclotomic polynomial.
