A single variable polynomial is represented as an arithmetic expression shown below: A0 + A1 * x + A2 * x 2 + + Ak * x k

The highest exponent, k, is called the degree of the polynomial, and the constants A0, A1, , Ak are the coefficients. For example, here are two polynomials with degree 3:

2.1 + 4.8x + 0.1x2 + (-7.1)x³

2.9 + 0.8x + + 1.7x³

Design, and implement a class for polynomials. The class may contain a static member constant, MAX, which indicates the maximum degree of any polynomial (this allows you to store the coefficients in an array with a fixed size).

The default constructor will be one which will initialize the polynomial with all coefficients set to zero. In addition, you must have another constructor that takes two parameters: degree, and coefficient_array which are used to initialize the polynomial appropriately. In addition you should have a member function that gets and sets the value of an appropriate coefficient. For example, get(k) returns the coefficient of xk , and set(k, 24.5) sets the coefficient of xk to 24.5. You should provide a member function for comparing two polynomials (whether they have same coefficients), and evaluating a polynomial value for specific value of x, say x = 5.7.

Please implement poly.cpp in (In C++ please) given the following poly.h header file:

#ifndef POLY_H

#define POLY_H

class poly

{

public:

static const int MAX = 10;

// CONSTRUCTORS

poly( );// a polynomial with degree 0

poly(const int k );// a polynomial with degree k

poly(const int k, const double initial_coeff[] );

// MEMBER FUNCTIONS

void set(const int k, const double coeff);// sets the kth coefficient

// CONSTANT MEMBER FUNCTIONS

int get(const int k ) const;// gets the kth coefficient

int degree() const;

double evaluate (const double xval) const;//evaluates the polynomial

private:

double data[MAX];

int degree;

};

}

#endif