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.
