Consider the list of operations below. choose the one that polynomials are not closed under. addition subtraction multiplication division

Polynomials form a system similar to the system of integers, and are not closed under division only. Note that the form of division in algebra is usually symbolized by the number line sign (which is also used for fractions), while the rest belong to the function of polynomials.

The correct answer is:

Division.

Explanation:

A monomial is a number, a variable, or the product of numbers and variables.  Anything with a radical or a negative exponent is not considered a monomial.

A polynomial is the sum or difference of one or more monomials.

When we divide numbers, sometimes they don't divide evenly, leaving us with a remainder, which we can write as a fraction or a decimal.

When we divide polynomials, a similar statement is true.  Sometimes they don't divide evenly, leaving us with a remainder, which we can write as a fraction.

However, when we write an algebraic expression with a variable as a fraction, this means the variable has a negative exponent.  As stated above, monomials cannot have negative exponents; this means the remainder term would not be a monomial.

If part of the solution is not a monomial, the entire solution is not a polynomial.

This means we divide two polynomials and may end with a solution that is not a polynomial; this means polynomials are not closed under division.