Question

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

Answer 1

This would be the closure property.

Answer 2

The difference between
`(6x^3 + x^2 - 4x + 9)` and
`(6x^3 + x^2 - 4x + 7)` is 2 .

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

We can see one more example

`(2x^2 -3)-(3x^2 +4) = -x^2-7`

So again we get a polynomial.

This property is called as the closure property.