Monomial

What is a Monomial?

A monomial is a mathematical expression consisting of only one term. This term can be a constant, a variable, or the product of constants and variables raised to non-negative integer exponents. Monomials are fundamental components in algebraic expressions and polynomials.

Single Term

A monomial contains only one term.

Constants and Variables

The term within a monomial can consist of constants (numerical values) and variables (symbols representing unknowns), possibly raised to non-negative integer exponents.

General Form

The general form of a monomial is $ax^n$ , where $a$ is a constant coefficient, $x$ is a variable, and $n$ is a non-negative integer exponent.

Examples of Monomials

Constant Monomial:
- $5$ is a monomial because it is a single term with no variables.
Variable Monomial:
- $x$ is a monomial because it is a single term representing a variable.
Constant Times Variable:
- $3y$ is a monomial because it is the product of the constant $3$ and the variable $y$ .
Variable with Exponent:
- $2x^3$ is a monomial because it consists of the variable $x$ raised to the exponent $3$ .
Product of Constants and Variables:
- $4ab$ is a monomial because it is the product of the constant $4$ , the variable $a$ , and the variable $b$ .
Constants with Exponents:
- $7c^2$ is a monomial because it is the product of the constant $7$ and the variable $c$ raised to the exponent $2$ .

Not Monomials

Sum of Terms:
- $2x+3y$ is not a monomial because it consists of two terms.
Negative Exponents:
- $4a^\text{-1}$ is not a monomial because it has a variable with a negative exponent.
Variables in Denominator:
- $\frac{5}{x}$ is not a monomial because it has a variable in the denominator.