Question

Is the set of monomials closed under multiplication? Which of the following gives a correct answer and an explanation?

A. Yes; the sum of any two monomials is a monomial.
B. No; the product of two monomials could be a polynomial..
C. Yes; the product of any two monomials is a monomial..
D. No; the product of two monomials could be a rational number.

Answer 1

The set of monomials is not closed under multiplication because the product of two monomials could be a polynomial.

Step-by-step explanation:

Option B is the correct answer: No; the product of two monomials could be a polynomial.

A monomial is an algebraic expression with one term, such as 5x or -2y^2. When you multiply two monomials, the result can sometimes have more than one term, which makes it a polynomial. For example, if you multiply 3x and 2y, the product is 6xy, which is a polynomial. Therefore, the set of monomials is not closed under multiplication.