Monomial
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A monomial is a type of polynomial that contains exactly one term. It can be a constant, a variable, or a product of constants and variables raised to non-negative integer powers.
The general form of a monomial is:
ax^n
Here, a is a constant (coefficient), x is the variable, and n is a non-negative integer exponent.
Examples of monomials include:
3x (a variable term with a coefficient)
5 (a constant term)
2x^2 (a term with a variable raised to a power)
-4y^3 (a term with a variable raised to a power and a negative coefficient)
The key characteristic of a monomial is that it consists of only one term.
The name "monomial" comes from the Latin word "mono-" meaning "one" and "nomial", derived from "nomen", meaning "term". Thus, "monomial" literally means "one term".
This name reflects the structure of a monomial, which consists of exactly one term. The term was coined in algebra to describe expressions with only one distinct term, whether it is a constant, a variable, or a product of constants and variables raised to some power.