(Solved): The conventional algorithm for evaluating a polynomial \( a_{n} x^{n}+a_{n-1} x^{n-1}+\ldots+a_{1} ...

The conventional algorithm for evaluating a polynomial \( a_{n} x^{n}+a_{n-1} x^{n-1}+\ldots+a_{1} x+a_{0} \) at \( x=c \) can be expressed in pseudocode by procedure polynomial \( \left(c, a_{0}, a_{1}, \ldots, a_{n}\right. \) : real numbers \( ) \) where the final value of \( y \) is the value of the polynomial at \( x=c \). a) Evaluate \( 3 x^{2}+x+1 \) at \( x=2 \) by working through each step of the algorithm showing the values assigned at each assignment step. b) Exactly how many multiplications and additions are used to evaluate a polynomial of degree \( n \) at \( x=c \) ? (Do not count additions used to incremen variable.)