The function a0 + a1 x x + a2 x x2 + a3 x x3 + ... + an x xn is a polynomial in x whose coefficients are the real numbers a0, a1, ..., an, where an is not zero. The number n is called the polynomial’s...

The function

a0 + a1 x x + a2 x x2 + a3 x x3 + ... + an x xn

is a polynomial in x whose coefficients are the real numbers a0, a1, ..., an, where an is not zero. The number n is called the polynomial’s degree.You can evaluate a polynomial at a given real value of x—call it x0—by computing the following sequence of numbers:

bn = an

bn-1 = an-1 + bn x x0

bn-2 = an-2 + bn-1 x x0

. . .

b0 = a0 + b1 x x0

The value of the polynomial is then b0. This way of evaluating a polynomial is called Horner’s method and requires n additions and n multiplications. Any other way of evaluating a polynomial will require at least this many additions and multiplications.

Write a program that reads a polynomial’s coefficients into an array and then evaluates it for various values of x, as entered by the user.