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

The conventional algorithm for evaluating a polynomial ancn$+$an$1$cn$1++$a$1$c$+$a$0$

a

n

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c

n

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$+$

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a

n

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$$

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$1$

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$$c

n

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$$

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$$

$1$

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$+$

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$+$

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a

$1$

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$+$

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a

$0$

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$$

at x $=$ c can be expressed in pseudocode by

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

power :$=1$

y :$=$ a$0$

for i :$=1$ to n

power :$=$ power $*$ c

y :$=$ y $+$ ai $*$ power

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

a

n

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c

n

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$+$

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a

n

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$1$

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$$c

n

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$$

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$1$

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$+$

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$+$

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a

$1$

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c

$+$

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a

$0$

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$\}$

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

n multiplications and $2$n additions

$2$n multiplications and n additions

n multiplications and n additions

$3$n multiplications and $2$n additions