Set of polynomials of degree less or equal than $n$ is equicontinuous (or compact) over every interval $[a,b]$ using Arzela-Ascoli theorem

Question

Define $\Pi=\{\text{polynomials of degree }\le n \text{ over } [a,b]\}$ with fixed $n$.

Norm is $\|f\|=\sup_{x\in D(f)}|f(x)| $

I am trying to proof that this set is equicontinuous using Arzela-Ascoli theorem, i.e. that every sequence $(P_n)$ in $\Pi$ has a convergent subsequence.

However, I am failing to see how this sequence is necessarily bounded. If it were, I could use a diagonal argument as in Arzela-Ascoli proof.

I have seen a similar question here: Is $K=\{f\mid f\in \Pi_n , \|f\|\le 1\}$ equicontinuous or not?

How about $P_n(x) = n x$?

Any hint (or solution) would be greatly appreciated.

My guess is that the homework question was missing information.