that for each j the derivative p' (r;) = 0. Show that the degree of p is at least 2m. (b) Let p(x) and d(x) be polynomials. Show that there is a pair of polynomials q(x) and r(x) with r(x) having degree strictly lower than that of d(x) so that p(x) = q(x)d(x) +r(x). Hint: This is polynomial division. d is the denominator, q the quotient and r the remainder. Prove this by fixing d(x) and using induction on the degree of p(x)