Which of the following statements about closure is false?

APolynomials are closed under addition. When you add polynomials, the result

will always be a polynomial.

BPolynomials are closed under subtraction. When you subtract polynomials, the result will always be a polynomial.
CPolynomials are closed under division. When you divide polynomials, the result will always be a polynomial.
DPolynomials are closed under multiplication. When you multiply polynomials, the result will always be a polynomial.

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.

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MsEHolt MsEHolt · Answer 2 · 2018-09-10T20:52:19-04:00

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.