Textbook Problem

Exercises 36—39 refer to the following algorithm to compute the value of a real polynomial.

Algorithm 11.3.3 Term-by-Term Polynomial Evaluation
[This algorithm computes the value of a polynomial $a\left[n\right]x^n+a\left[n-1\right]x^{n-1}+\cdots +a\left[2\right]x^2+a\left[1\right]x+a\left[0\right]$by computing each term separately, starting with $a\left[0\right]$ , and adding it to an accumulating sum.]Input: n [a nonnegative inreger], $a\left[0\right],a\left[1\right],a\left[2\right],\dots a\left[n\right]$
[an array of real numbers], x [a real number]Algorithm Body:
$polyval:=a\left[0\right]$ for $i:=1$to n $term:=a\left[i\right]$ for $j:=1$ to i $term:=term\cdot x$ next j $polyval:=polyval+term$next i $\begin{array}{l}[Atthispointpolyval=a\left[n\right]x^n+a\left[n-1\right]x^{n-1}\\ +\cdots +a\left[2\right]x^2+a\left[1\right]x+a\left[0\right].]\end{array}$
Output: polyval [a real number] 37. Trace Algorithm 11.3.3 for the input $n=2,a\left[0\right]=5,a\left[1\right]=-1,a\left[2\right]=2$ , and $x=3$