Rewrite the Pseudocode for Horner's method in either C$++,$ Java, or Python. Test it by using the function used in the notes when deriving what Horner's Method would look like, $f(x)=-1+5x-3x^2+3x^3+2x^4$ by evaluating it at $x=0\mathrm{.}5$ to get $P(0\mathrm{.}5)=1\mathrm{.}25.$ Include your rewritten code in the HW you turn in$.$

For the polynomial $P(x)=8-3x^2+2x^4+8x^6-2x^8+3x^{10},$

$($a$)$ How many additions and multiplications would Horner's method use to evaluate $P(0\mathrm{.}1)?$

$($b$)$ What function call would you write to use the Horner's method function you wrote in problem $5$ in order to evaluate $P(0\mathrm{.}1)?$

$($c$)$ How many times would using Horner's method directly here waste time adding $0?$

For the polynomial $P(x)=4x+5x^3+7x^5+9x^7-x^9+4x^{11},$

$($a$)$ How many additions and multiplications would Horner's method use to evaluate $P(0\mathrm{.}1)?$

$($b$)$ What function call would you write to use the Horner's method function you wrote in problem $5$ in order to evaluate $P(0\mathrm{.}1)?$

$($c$)$ How many times would using Horner's method directly here waste time adding $0?$

Using the Horner's method function given in the notes, consider the following call to Horner's method. Horners $([2,4,-3,8,-5,6],0\mathrm{.}2)$

$($a$)$ What degree polynomial is being inputted into the function in array form?

$($b$)$ How many multiplications and additions will the Horner's method function do$?$

Using the Horner's method function given in the notes, consider the following call to Horner's method.

Horners $([1,-5,2,7,2,-8,9,-2],0\mathrm{.}2)$

$($a$)$ What degree polynomial is being inputted into the function in array form?

$($b$)$ How many multiplications and additions will the Horner's method function do$?$