Let In be the set of real polynomials of degree at most n, and write p' for the derivative of p. Show that 5 = PEP6 : P(-8) = -9p'(-8) is a subspace of 6. 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