Factorize $2a^3 - b^3 - c^3$ I need to factorize the expression $2a^3 - b^3 - c^3$. I see that one zero is achieved when $a=b=c$, but I can't find the factor(s).
I assume you're looking for factors that are polynomials with integer coefficients.

Your polynomial is not factorizable in this sense. To see why, look at what happens when $b=0,c=1$. You get $2a^3-1$, which you cannot factor over the integers.
$$2X^3-b^3-c^3=0$$

So $X=\sqrt[3]{\frac {b^3+c^3} 2}$ is a root, now do long division and use the quadratic formula.