Help with Polynomial Class and Dynamic Arrays

[bmakloski]

Hello, I am doing an assignment for my 2nd year programming class. I am supposed to create a program that can add, subtract, and multiply polynomials and constants. I need help overloading my arithmetic operators as well as my << and >> operators. If someone could also take a look at what I have so far and make sure that it looks good and makes sense, that would be really helpful. I'm still pretty new so I might need the vocab to be simplified haha. My original thought process is that I could use the dynamic array where the size and index number of the array will be the degrees so a[2] would be X^2 and and a[0] refers to a constant, then the actual value stored at that index place would be the coefficient of the x term. Here is what my class structure looks like, as well as the functions that I have already attempted to code.

#include<iostream>
#include<cstdlib>
using namespace std;

typedef int* IntPtr;
class polynomial
{
public: 
	polynomial(int degree_Size, int coefficient[]);
	polynomial();//sets degreeSize to 10
	polynomial(const polynomial& polynomailObject);//copy constructor
	void input();
	polynomial& operator = (const polynomial& rightSide);
	~polynomial();
	friend const polynomial operator +(const polynomial& number1, const polynomial& number2);
	friend const polynomial operator -(const polynomial& number1, const polynomial& number2);
	friend const polynomial operator *(const polynomial& number1, const polynomial& number2);
	friend istream& operator >> (istream& inputStream, polynomial newNumber);
	friend ostream& operator <<(ostream& outputStream, const polynomial& number);
	int getDegreeSize()const { return degreeSize; }
private: 
	int degreeSize;
	int *privateCoefficient;
};
polynomial::polynomial(int degree_Size,int coefficient[])
{
	degreeSize = degree_Size;
	privateCoefficient = new int[degreeSize];
	for (int i = 0; i < degreeSize; i++)
	{
		privateCoefficient[i] = coefficient[i];
	}
}
polynomial::polynomial()
{
	degreeSize = 10;
	privateCoefficient = new int[degreeSize];
}
polynomial::~polynomial()
{
	if (privateCoefficient)
	{
		delete [] privateCoefficient;
		privateCoefficient = NULL;
	}
}
polynomial::polynomial(const polynomial& polynomialObject):degreeSize(polynomialObject.getDegreeSize())
{
	privateCoefficient= new int[degreeSize];
	for (int i = 0; i < degreeSize; i++)
	{
		privateCoefficient[i] = polynomialObject.privateCoefficient[i];
	}
}
polynomial& polynomial::operator = (const polynomial& rightSide) {
	if (this == &rightSide)
	{
		return *this;
	}
	else
	{
		degreeSize = rightSide.degreeSize;
		delete[] privateCoefficient;
		privateCoefficient = new int[degreeSize];
		for (int i = 0; i <= degreeSize; i++)
		{
			privateCoefficient[i] = rightSide.privateCoefficient[i];
		}
		return *this;
	}
}
istream& operator >> (istream& inputStream, polynomial& newNumber)
{
	int degreeSize;
	int *privateCoefficient;
	cout << "Please enter the highest degree of your polynomial: X^";
	cin >> degreeSize;
	privateCoefficient = new int[degreeSize];
	for (int i = 0; i <= degreeSize; i++)
	{
		cout << "Please enter the coefficient for term X^" << i << endl;
		cin >> privateCoefficient[i];
	}

}

If you see any logic flaws please let me know. I want this to be done right and I want to learn. I am welcome to your teaching!