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1 (a) Let 10(3) be a polynomial with real coefcients. Suppose that it has in real roots r1, . . . rm. Suppose that for each j the derivative p'(rj) = 0. Show that the degree of p is at least 2173.. (b) Let p(:1:) and d(m) be polynomials. Show that there is a pair of polynomials (1(3) and 111:) with 112:) having degree strictly lower than that of 03(3) so that p(:r) : q(:r)d(:r) + rs). Hint: This is polynomial division. (1 is the denominator, q the quotient and 1' the remainder. Prove this by xing (1(3) and using induction on the degree of 11(3)