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 $a_n{x}^n+a_{n-1}{x}^{n-1}+$cdots$+a_{1}x+a_0$ at $x=c.$

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

$y$:$=a_n$

for $i$:$=1ton$

$,y$:$=y^{**}c+a_{n-i}$

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

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

Multiple Choice

$2$n multiplications and $n$ additions

$n$ multiplications and $2n$ additions

$2n$ multiplications and $2n$ additions

$n$ multiplications and $n$ additions