Which property of polynomial subtraction says that the difference of two polynomials is always a polynomial?

The answer is the closure property of polynomials. The closure property says that polynomials are closed under addition, subtraction, and multiplication, which means that every time that you add, subtract, or multiply polynomials the result is always another polynomial. 

In our case, the closure property of polynomials for subtraction states that every time you subtract two or more polynomials, the result of that subtraction is always a polynomial.