There is a more efficient algorithm (in terms of the number of multiplications and additions used) for evaluating polynomials, than the conventional algorithm described in the previous exercise. It is called Horners method. There is a more efficient algorithm (in terms of the number of multiplications and additions used) for evaluating polynomials, than the conventional algorithm described in the previous exercise. It is called Horners method. The following pseudocode shows how to use this method to find the value of a_nxⁿ + a_n?1x^n?1 + + a1x + a0 at x = c. procedure Horner(c, a0, a1, a2, . . . , an: real numbers y := an for i := 1 to n y := y ? c + an?i {y = a_ncⁿ + a_n?1c^n?1 + + a1c + a0} a) Evaluate p(x) = x³+3x² + x + 1 at x = 2 by working through each step in the algorithm.

b) Exactly how many multiplications and additions are used by this algorithm to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.)