The conventional algorithm for evaluating a polynomial $a_n{c}^{11}+a_{n-1}{c}^{c^{11}}+$cdots$+a_{1}c+a_0$ at $x=c$ can be expressed

in pseudocode by

procedure polynomial$(c,a_0,a_1,$dots,$a_n$ real numbers$)$

power :$=1$

$y$:$=a_0$

for $i$:$=1$ to $n$

power:$=$ power$*c$

$y$:$=y+a_i^{**}$ power

return $y\{y=a_n{c}^n+a_{n-1}{c}^{n-1}+$cdots$+a_{1}c+a_0\}$

where the final value of $y$ is the value of the polynomial at $x=c.$

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

Multiple Choice

$2n$ multiplications and $n$ additions

$n$ multiplications and $n$ additions

$3n$ multiplications and $2n$ additions

$n$ multiplications and $2n$ additions