OSN 2022 Problem 2

Let $P(x)$ be a polynomial with integer coefficient such that $P(1) = 10$ and $P(-1) = 22$ . (a) Give an example of $P(x)$ such that $P(x) = 0$ has an integer root. (b) Suppose that $P(0) = 4$ , prove that $P(x) = 0$ does not have an integer root.