You want to show that the given set is not a subspace of

. Recall the definition of a vector subspace. You need to show that one of the vector subspace axioms does not hold in this case; that is, you need to give a counter example to one of the axioms.

No. You need to show that the given set is a subspace of

. Again, recall the axioms of vector space and show that they hold for any polynomials in your set S.

I'll start with closure to addition: Let

. Then

by definition of S. Now, note that

, that is,

and so by definition of S,

Can you do the rest?