Let P2 denote the vector space of all polynomials with degree less than or equal to 2. (a) Show that B = {1 + x + x 2 , 1 + 2x − x 2 , 1 − 2x − x 2} is a basis for P2. (b) Find the coordinate vector of p(x) = 1 + 2x + 3x 2 relative to the basis B.