Question 78
For each non-constant integer polynomial $P(x)$, let's define
$$
M_{P(x)} = \max_{x \in [0; 2021]} |P(x)|.
$$
1. Find the minimum value of $M_{P(x)}$ when $\deg P(x) = 1$.
2. Suppose that $P(x) \in \mathbb{Z}[x]$ when $\deg P(x) = n$ and $2 \le n \le 2022$. Prove that $M_{P(x)} \ge 1011$.
$$
M_{P(x)} = \max_{x \in [0; 2021]} |P(x)|.
$$
1. Find the minimum value of $M_{P(x)}$ when $\deg P(x) = 1$.
2. Suppose that $P(x) \in \mathbb{Z}[x]$ when $\deg P(x) = n$ and $2 \le n \le 2022$. Prove that $M_{P(x)} \ge 1011$.