Problem

Source: 2016 Saudi Arabia BMO TST , level 4, III p3

Tags: polynomial, Integer Polynomial, algebra



Does there exist a polynomial $P(x)$ with integral coefficients such that a) $P(\sqrt[3]{25 }+ \sqrt[3]{5}) = 220\sqrt[3]{25} + 284\sqrt[3]{5}$ ? b) $P(\sqrt[3]{25 }+ \sqrt[3]{5}) = 1184\sqrt[3]{25} + 1210\sqrt[3]{5}$ ?