Problem 10 (10 points). The conventional algorithm for evaluating a polynomial at z = c ca n be expressed in pseudocode by Algorithm 1 Polynomial Evaluation 1: procedure PolynOMIAL(ao, a1,...,an,c) 2: power1 for i := 1 to n do 4: 5: 6: 7: powerpowerc yyai *power return y where the final value of y is the value of the polynomial at c. (a) Evaluate 3z2 +z+1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. (b) Exactly how many multiplications and additions are used to evaluate a polynomial of degree n at c? Do not count additions used to increment the loop variable.) Problem 11 (10 points). Suppose that a, b, c, m E Z such that m 2 2 and c > 0. Prove that if ab (mod m), then ac bc (mod me)