Question

Polynomials are closed under the operation of multiplication. Which statement best explains the meaning of closure of polynomials under the operation of multiplication?

Answer 1

Answer:

When any two polynomials are subtracted, the result is always a polynomial.

Answer 2

The list of choices is missing so I am going to give my wording:

The fact that a set closed under a certain operation means that when the operation is applied to any element(s) of the set, the result will be also an element of the same set (as opposed to something that does not belong to the set).

In this case the set contains all polynomials. Multiplying any two polynomials results in another polynomial, therefore this set is closed with respect to multiplication. In contrast, the set is not closed with respect to division. Dividing two polynomials may lead to non-polynomial expressions with non-integer powers and so the set is not closed under division.