Which of the following statements about closure is false?

A: Polynomials are closed under addition. When you add polynomials, the result will always be a polynomial.
B: Polynomials are closed under subtraction. When you subtract polynomials, the result will always be a polynomial.
C: Polynomials are closed under division. When you divide polynomials, the result will always be a polynomial.
D: Polynomials are closed under multiplication. When you multiply polynomials, the result will always be a polynomial.