# Which of the following statements about closure is false?

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## Question:

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.

## Answer:

The correct answer is:

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

Explanation:

When you divide polynomials, there are times that one polynomial does not divide evenly by the other.  In these cases, we have a remainder, in which we have a variable in the denominator.  This remainder is not a monomial, since the variable would have a negative power (since it is in the denominator); this means the quotient is not a polynomial.

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