I have the following polynomial $f(x)=x^6-15x^4-14x^3 + 75x^2-210x-76$ for which I know that $\sqrt[3]{7} + \sqrt{5}$ is a root. I guessed $\sqrt[3]{7} - \sqrt{5}$ is also a root, and most probably the rest are complex. But I have no idea how to compute the Galois group of this polynomial. I know some methods for quartic, cubic and quadratic polynomials, but not for higher degree powers. Can anyone help me? Thank you!
2026-03-27 15:36:08.1774625768
Computing the Galois group of polynomials of high degree
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