Question

Consider the following program specification for evaluating a polynomial anxh + an- xn-1 + ... + a1x + ao at x = c: Input: c, 20, 21, ..., an ER Output: anch + an-1ch-1 + ... + a1c + ao Consider the following two implementations of this program specification: Implementation 1: Polynomial_1 Polynomial_1(c, 20, 21, ..., an) (1) it 1 (2) yt-20 (3) whileisn (4) yey+a; * Power(c, i) (5) it i+1 (6) return y where Power is implemented as follows: Power(a, b) (1) ito (2) yr1 (3) while i < b (4) yey* a
Please answer the 2 blanks in Q1, show full working!! I want to know how this works, thanks. This is a discrete math question.

Answer 1

For polynomial_1

The first time it is executed is when i=1, y=a(0)=1 (constant term) so that $y={\color{Red} 3}$

The second time it is executed is when

y + y +a; * Power(c, i) = 3+2* Power(3,1)

Which is

y = 3+2+31 = 3+2:3=9

This algorithm is called Horner's method for polynomial evaluation

$\blacksquare$

Hope this was helpful. Please do leave a positive rating if you liked this answer. Thanks and have a good day!