The following is a homework problem:
For a fixed $a \in \mathbb{R}$, determine the dimension of the subspace of $P_n(\mathbb{R})$ (the vector space of polynomials of at most degree $n$) defined by: $W = \{f \in P_n(\mathbb{R})\,|\, f(a) = 0\}.$
I can't imagine what the basis would look like for $W$ though. Or do I not even need the basis? Can I figure out the dimension without knowing the basis?
Could you give some helpful hints or a framework for solving this and similar problems?
Note: I'm not looking for the answer itself since this is homework.