Which of the following statements about closure is false?

Question

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

Answer 1

Polynomials are closed under division. When you divide polynomials, the result will always be a polynomial.

This statement is false. Polynomial division may result in a quotient that is not a polynomial, but a rational function.