Can someone help me solve this question please. Show me the steps with an explanation, thank you.

Let I'm be the set of real polynomials of degree at most n. Show that S={PEP6 : P(1) =P(-9) = 0} is a subspace of P6- To check that you are on the right track, answer the following questions. . Is S a subset of a known vector space? Yes . Does S contain the zero element? Yes . Is S closed under vector addition? Yes . Is S closed under scalar multiplication? Yes