Chapter 7, Problem 12E

Create a class polynomial that is used to evaluate a polynomial function of x:

P(x) = a₀ + a₁x + a₂x + ⋯ + a_n−1xⁿ⁻¹ + a_nxⁿ

The coefficients a_i are floating-point numbers, the exponents of x are integers, and the largest exponent n—called the degree of the polynomial—is greater than or equal to 0. The class has the attributes

■    degree —the value of the largest exponent n

■    coefficients —an array of the coefficients a_i

and the following methods:

• Polynomial (max) —a constructor that creates a polynomial of degree max whose coefficients are all 0
• setConatant (i, value) —Sets the Coefficient a_i to value
• evaluate (x) — returns the value of the polynomial for the given value x

For example, the polynomial

P(x) = 3 + 5x + 2x³

is of degree 3 and has coefficients a₀ = 3, a₁ = 5, a₂ = 0, and a₃ = 2. The invocation evaluate (7) computes 3 + 5 × 7 + 0 × 7 + 2 = 7³, which is 3 + 35 + 0 + 686, and returns the result 724.