Using dynamic arrays, implement a polynomial class with polynomial

addition, subtraction, and multiplication.

Discussion: A variable in a polynomial does very little other than 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

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. Where is the term in x*x in the previous

example? 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 polynomial techniques.

Unless you already know these techniques, or learn very quickly, don’t

use these techniques.

Provide a default constructor, a copy constructor, and a parameterized

constructor that enables an arbitrary polynomial to be constructed. Also

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.