We can prove by induction that there exist no more than roots. n Suppose that such that . Then , where . Theorem 4.6 (Division Let and be polynomials of degree and Theorem): n m, where 1mn. Then of degree and a unique polynomial of degree or less nm m1 such that . Evaluating Polynomials How do we compute ? We may need to make a change of variables: , which leads to . Using Theorem we know that Taylor’s
We can prove by induction that there exist no more than n roots. Suppose that such that . Then , where . Theorem 4.6 (Division Theorem): Let and be polynomials of degree n and m, where 1mn. Then of degree nm and a unique polynomial of degree m1 or less such that . Evaluating Polynomials How do we compute ? We may need to make a change of variables: , which leads to . Using Taylor’s Theorem we know that
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