that tor each 3 the derlvatlve p' m ) = U. snow that the degree or p is at least 2m. (0) Let pm) and d(:1:) be polynomials. Show that there is a pair of polynomials q(x) and r(m) With r(x) having degree strictly lower than that of d(m) so that p(a:) = q(:r,)d(a:) + r(a;). Hint: This is polynomial division. d is the denominator, q the quotient and r the remainder. Prove this by xing d(a:) and using induction on the degree of p(.'1:)