Please answer below questions.

Let L : P4 - P4 be the map defined by L(p) = L(p(x)) = x2p"(x) - 2p(x) - 5p'(x) (where P4 denotes the vector space of polynomials with real coefficients of degree less than 4). 1. Find a matrix A satisfying sL(p) = A * Sp, where S = {1, x, x2 , x3} is the standard basis for P4 2. Using 1, explain why this implies L is a linear transformation. 3. Find a basis for ker(L). 4. Find a basis for im(L)