1. Polynomials are closed under addition because the addition of two polynomials gives always as result a new polynomial
2. Polynomials are closed under subtraction because the subtraction between two polynomials gives always as result a new polynomial
3. Polynomials are closed under multiplication because the multiplication between two polynomials gives always as result a new polynomial
4. Polynomials are not closed under division. For example:
[tex]\frac{x+1}{x^2}=\frac{x}{x^2}+\frac{1}{x^2}=\frac{1}{x}+\frac{1}{x^2}[/tex]The result is not a polynomial.
