/sci/ - Science & Math

So, I've got a Linear Algebra assignment and the last week of material is leaving me a touch confused, maybe because it is so abstract idk.

I am stuck on these 2 sub-questions:
4. Prove U = {f|f(x + π) = f(x), f ∈ C(-∞,+ ∞)} is a subspace of C(-∞,+ ∞)
5. Prove V = {p(x)|p(1)=0,p(x) ∈ Pn} is a subspace of Pn

Any help/pointers in the right direction?