Using dynamic arrays, implement a polynomial class with polynomial addition, subtraction, and multiplication. Discussion: A variable in a polynomial does nothing but act as a placeholder for the coefficients. Hence, the only interesting thing about polynomials is the array of coefficients and the corresponding exponent. Think about the polynomial

x*x*x + x + 1

Where is the term in x*x? One simple way to implement the polynomial class is to use an array of doubles to store the coefficients. The index of the array is the exponent of the corresponding term. If a term is missing, then it simply has a zero coefficient.

There are techniques for representing polynomials of high degree with many missing terms. These use so-called sparse matrix techniques. Unless you already know these techniques, or learn very quickly, do not use these techniques.

Provide a default constructor, a copy constructor, and a parameterized constructor that enables an arbitrary polynomial to be constructed.

Supply an overloaded operator = and a destructor. Provide these operations:

polynomial + polynomial, constant + polynomial, polynomial + constant, polynomial - polynomial, constant - polynomial, polynomial – constant. polynomial * polynomial, constant * polynomial, polynomial * constant, Supply functions to assign and extract coefficients, indexed by exponent. Supply a function to evaluate the polynomial at a value of type double.

You should decide whether to implement these functions as members, friends, or standalone functions.