1. Polynomials are closed under the operations of addition and substraction mean that:
If we add two polynomials, the result is still a polynomial (so still in the set of polynomials)
Also, If we subtract 2 polynomials, the result is a polynomial.
2. Example: given the polynomials :
and 
Addition example:
Subtraction example:
=
=
So both M(x)+N(x) and N(x)-M(x) are polynomials
If we add two polynomials, the result is still a polynomial (so still in the set of polynomials)
Also, If we subtract 2 polynomials, the result is a polynomial.
2. Example: given the polynomials :
Addition example:
Subtraction example:
=
=
So both M(x)+N(x) and N(x)-M(x) are polynomials