Minimal polynomial over $\mathbb Q(\sqrt{-2})$ 
Find the minimal polynomial for $\sqrt[3]{25} - \sqrt[3]{5} $ over  $\mathbb Q$ and $\mathbb Q(\sqrt{-2})$.

I have done the first part of this, over $ Q$, and have a polynomial. But I do not know how to do this over $ Q \sqrt{-2}$

$f(x) = x^3 + 15x - 20$ is still a polynomial over $\Bbb Q(\sqrt{-2})$ with $\sqrt[3]{25}-\sqrt[3]{5}$ as a root. The minimal polynomial you are looking for therefore has to be a factor of $f$. Can you find those factors (over, say $\Bbb C$)? Are there any of them (apart from $f$ itself) that both is a polynomial over $\Bbb Q(\sqrt{-2})$ and have $\sqrt[3]{25} - \sqrt[3]5$ as a root?
