We say that a polynomial with real coefficients p(x) is of degree d if we can write i) = aqx + ag_12% 1 + ... + ao, with aq # 0. Prove by induction on n that if p(x) is a polynomial of degree n and f(x) is a polynomial of degree d > 1 then there are polynomials (z) and r(z) with the degree of r strictly less than d so that p(x) = q(z)f(z) + r(z). Hint: This is called polynomial division. (x) is called the quotient and r(x) is called the remainder. The way you set up the algorithm for division is that you pick the z"~% term in g(z) to cancel the 2 term in p(z)