Please help me to understand with a very detailed solution

4) Let J: P2 - P2 be the mapping such that, for all pe P2, Jp(z) = (12 +1)p"(z) + (3x + 2)p' (z) Then J is a linear mapping and you may assume so here. a) Let B = {po, P1, P2), where po(r) = 1, pi(z) = z, and pz(x) = x2. Find the matrix A representing J relative to B. b) Let D = (90, 91, 92), where 90(3) = 1+2x+32, 91(2 ) = -1+2+x2, 92(x) = 3+ 1+z Then D is a basis for P2 and you may assume so here. Find the matrix M represent- ing J relative to D