Is the difference of two polynomials always a polynomial?

Let's try an example:

The difference between (6x3 + x2 - 4x + 9) and (6x3 + x2 - 4x + 7) is 2 .

2 is a polynomial of degree 0, so this example would appear to support the hypothesis in the question.

However, polynomials cannot include negative exponents. So, (2x)/(2x2) produces 1/x, which is not a polynomial.

So no, not always.