Question

i=n Consider the following procedure to evaluate a polynomial a;x' at x = C. i = 0 procedure poly(ca ,...an power + 1 y cao for i from iton power + power * y+y+a; power return y where + denotes assignment, * denotes multiplication. Evaluate 3x2 + x + 1 at x = 2 by stepping through the algorithm.

Answer 1

Answer:)

First, power is set to 1

y is set to

I = Op

for i from 1 to 2 (since n = 2)

i = 1

• power is set to power * c = 1 * 2 = 2
• y is set to y + $a_1$ * power = 1 + 1 * 2 = 1 + 2 = 3

i = 2

• power is set to power * c = 2 * 2 = 4
• y is set to y + $a_2$ * power = 3 + 3 * 4 = 3 + 12 = 15

i = 3, and thus exit the loop.

return y = 15.

Thus the algorithm returns the value of y = 15 at x = 2, which is what is required.