1. Implement Horners method for calculating a polynomial of degree n given a value of x and all of the coefficients (the a_i terms) using an array of type double:

a_nxⁿ + a_n-1x^n-1 + a_n-2x^n-2 + + a₂x² + a₁x + a₀

where n is a positive int and a_n 0.

Prompt the user: 1) for the degree n (a positive int), 2) for the n+1 coefficients (of type double, beginning with a_n and ending with a₀), and 3) for the value of x (of type double). The algorithm is as follows (the final value of the polynomial evaluated at x is b₀):

b_n = a_n;

b_n-1 = a_n-1 + b_nx;

b_n-2 = a_n-2 + b_n-1x;

b₁ = a₁ + b₂x;

b₀ = a₀ + b₁x;

You do not have to defensively code for user errors. It is recommended that you use 2 arrays: one for the a_is and one for the b_is. You may use a recursive algorithm or a standard loop. Display the result to the user.

Example: f(x) = y = 2x² 3x + 1 is a second-degree polynomial (n = 2), where a₁ = 2, a₂ = -3, and a₃ = 1. Evaluate the polynomial at x = -1 using Horners method; note that f(-1) =

2 *( -1)² +( -3) *( -1) + 1 = 2 + 3 + 1 = 6. The array of a_is is:

The a array	1	-3	2	0
Index	0	1	2	. . .

Using Horners algorithm, we get:

b₂ = a₂ = 2

The b array	0	0	2	0
Index	0	1	2	. . .

b₁ = a₁ + b₂ * x = -3 + 2 * -1 = -3 + -2 = -5

b array	0	-5	2	0
Index	0	1	2	. . .

b₀ = a₀ + b₁ * x = 1 + -5 * -1 = 1 + 5 = 6, and 6 is the final answer.

b array	6	-5	2	0
Index	0	1	2	. . .