Problem 1. Given a polynomial p(x) = anx n + an1x n1 + + a1x + a0, where the coefficients are ai s, Horners method is an efficient algorithm for evaluating the polynomial at a number c that works as follows: Multiply an by c, then add an1. Then multiply the result by c and add an2. Then multiply the result by c and add an3 and so on until you reach a0. This over all gives an O(n) algorithm for evaluation of p(c). Apply Horners method to the polynomial p(x) = 5x 3 2x 2 + 3x 7 at c = 2. How many multiplications and additions?

Problem 1. Given a polynomial p(x)-an"+ an-12-1az +ao, where the coefficients are ai's, Horner's method is an efficient algorithm for evaluating the polynomial at a number c that works as follows: Multiply an by c, then add an-1. Then multiply the result by c and add an-2. Then multiply the result by c and add an-3 and so on until you reach ao. This over all gives an O(n) algorithm for evaluation of p(c). Apply Horner's method to the polynomial p(x) 5-2r23r 7 at c 2. How many multiplications and additions