Determine whether S is a subspace of V

Where S and V are defined as below. I am not sure how to solve this problem. Could someone please explain it to me? Thanks!

S = { f(x) E P3 | f(0) + f(1) = 2 }, V = P3

A note on notation: The capital E is an epsilon, indicating that f(x) is an element of P3
For the P3, 3 should be a subscript

The zero vector in P3 is the polynomial g defined by g(x)=0 for all x. So, g(0)+g(1)=0+0=0, so g(0)+g(1) is not equal to 2, meaning g(x) is not in S. Since S does not contain the zero vector, it is not a subspace of P3. Hope that helps :)