Difficult# Finite Dimension: Known-Root Polynomial Subspace

LINALG-K$VVNV

Let $\mathcal{P}_n$ denote the set of all real-coefficient polynomials of degree at most $n$. This is a finite-dimensional vector space. Let $c\in \mathbb{R}$ be an arbitrary, fixed scalar value. Let $W = \{f(x) \in \mathcal{P}_n\mid f(c) = 0\}$, which is a subspace of $\mathcal{P}_n$. What is $\dim(W)$?