Monomial
Table of Contents
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.
Related Links
Arithmetic Sequence
Complex Number
Factor
Irrational Number