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 1

The correct answer for the question that is being presented above is this one: "C. Polynomials are closed under division. When you divide polynomials, the result will always be a polynomial." Polynomials are NOT closed under division.

Answer 2

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.