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

!

P(x) = a0 + a1x + a2x2 +!+ an"1xn"1 + anxn . The coefficients ai 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 zero. The class has the attributes

• degree—the value of the largest exponent n

• coefficients—an array of the coefficients ai

and the following methods:

• Polynomial(max)—a constructor that creates a polynomial of degree max whose

coefficients are all zero

• setConstant(i, value)—sets the coefficient ai to value

• evaluate(x)—returns the value of the polynomial for the given value x

For example, the polynomial

P(x) = 3 + 5 x + 2 x3 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 " 72 + 2 " 73 = 3+ 35 + 0 + 686 = 724 and returns

the result 724. A possible dialogue between the program and the user follows:

Constructing a polynomial:

3+ 5x + 2x^3

Evaluating the polynomial at 0 should give 3

Got: 3.0

Evaluating the polynomial at 1 should give 10

Got: 10.0

Evaluating the polynomial at 7 should give 724

Got: 724.0

Evaluating the polynomial at 1/2 should give 5.75