B. a) Consider the polynomial P(x) = xm(x -1)" (som > 0 and n 2 0). List all polynomials that can be constructed this way so that degree (P(x) ) = 5. b) For P(x) = x"(x - 1)(x -2). List all polynomials that can be constructed this way with degree 3. c) For P(x) = x. List all polynomials that can be constructed this way with degree 4. d)* Evaluate C(6,1), C(5,2), and C(1,0) and compare your answers to the size of your lists from a), b, c) (Hint: there should be an OBVIOUS comparison!) e)* Without listing them all, determine how many polynomials of the form R(x) = x" (x - 1)(x - 2)(x - 3) can be constructed so that degree(R(x) ) = 10. Hint: you can find the number of polynomials of degree D using k different factors using a combination formula of the form C(M, N). The trick is to find how M and N relate to D and k