The difference between [tex] (6x^3 + x^2 - 4x + 9) [/tex] and [tex] (6x^3 + x^2 - 4x + 7) [/tex] 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
[tex] (2x^2 -3)-(3x^2 +4) = -x^2-7 [/tex]
So again we get a polynomial.
This property is called as the closure property.
