Let P be the space of all polynomials with real coefficients. Determine which of the following subsets of P are subspaces: (a) S1 = {p(x) : p(1) = 0} (b) S2 = {p(x) : degree of p(x) = 3} (c) S3 =...

Let P be the space of all polynomials with real coefficients. Determine which of the following subsets of P are subspaces:

(a) S1 = {p(x) : p(1) = 0}

(b) S2 = {p(x) : degree of p(x) = 3}

(c) S3 = {p(x) : degree of p(x) ≤ 3}

(d) S4 = {p(x) : constant term is zero}