The conventional algorithm for evaluating a polynomial anxn + an−1xn−1 +· · ·+a1x + a0 at x = c can be expressed in pseudocode by
procedure polynomial(c, a0, a1, . . . , an: real numbers)
power := 1
y := a0
for i := 1 to n
power := power ∗ c
y := y + ai ∗ power
return y {y = ancn + an−1cn−1 +· · ·+ a1c + a0}
where the final value of y is the value of the polynomial at x = c.
a) Evaluate 3x2 + x + 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 x = c? (Do not count additions used to increment the loop variable.)