Find a monic cubic polynomial P(x) with integer coefficients such that $P(\sqrt[3]{4} + 1) = 0$ . (A polynomial is monic if its leading coefficient is 1.)
This question has been asked before. See a solution at https://web2.0calc.com/questions/polynomial_80#r1. You may also want to see https://web2.0calc.com/questions/hard-algebra_17#r1 which solves this kind of problem but it has more explicit details. If you don't understand some steps, ask.