NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

There is a more efficient algorithm $($in terms of the number of multiplications and additions used$)$ for evaluating polynomials than the conventional algorithm. It is called Horner's method. This pseudocode shows how to use this method to find the value of anxn $+$ an $1$xn $1++$ a$1$x $+$ a$0$ at x $=$ c$.$

procedure Horner$($c$,$ a$0,$ a$1,...,$ an: real numbers$)$

y :$=$ an

for i :$=1$ to n

y :$=$ y $*$ c $+$ an $$ i

return y$\{$y $=$ ancn $+$ an $1$cn $1++$ a$1$c $+$ a$0\}$

Exactly how many multiplications and additions are used to evaluate a polynomial of degree n at x $=$ c$?$