Given polynomial $x^3 + t^2x− t^3$ over $k$, where $k = C(t)$ is the field of rational functions in one variable over complex numbers C.
This problem comes from Johns Hopkins University Spring 2010 algebra qualifying.
I think the splitting field of this polynomial is $C(t)$ itself, since the three root of the polynomial is the three root of $x^3+x-1=0$ times $t$. So the Galois group shall be trivial group. But this look like such a easy problem that I believe some parts goes wrong.