Find the minimal polynomial over Q of
11+sqrt3(13)
\(x-(11+\sqrt[3]{13}) = 0 \\ x - 11 = \sqrt[3]{13} \\ \text{now cube both sides} \\ x^3-33 x^2+363 x-1331 = 13 \\ x^3-33 x^2+363 x-1318 = 0\)
