Question 14
Let $\alpha$ be a real number. Determine all polynomials $P$ with real coefficients such that
$$
P(2x+\alpha) \leq (x^{20} + x^{19}) P(x)
$$
holds for all real numbers $x$.
$$
P(2x+\alpha) \leq (x^{20} + x^{19}) P(x)
$$
holds for all real numbers $x$.