I need to make a polynomial ADT using the LIST ADT in C, not C++, that can accomplish the following functions:

1. Evaluate( p(x), z ). Evaluates the polynomial p(x) at the point x = z and returns the result.

2. Add( ( ) 1 p x , ( ) 2 p x ). Returns the polynomial that results when ( ) 1 p x is added to ( ) 2 p x .

3. Subtract( ( ) 1 p x , ( ) 2 p x ). Returns the polynomial that results when ( ) 1 p x is subtracted from ( ) 2 p x .

4. Multiply( ( ) 1 p x , ( ) 2 p x ). Returns the polynomial that results when ( ) 1 p x is multiplied by ( ) 2 p x .

5. Differentiate( p(x)). Returns the polynomial that results when p(x) is differentiated.

I'm at a loss for where to start with this. How can this be done?