Monomial

A Monomial is a single term algebraic expression consisting of a number (coefficient), one or more variables, and non-negative integer exponents. The term is a product of a coefficient and variables raised to non-negative integer powers. Monomials can be constants, variables, or products of constants and variables. They are fundamental building blocks of polynomials, which are sums of monomials. The key characteristic is the absence of addition or subtraction operations separating the terms within the expression; it must be a single entity created through multiplication and exponentiation.

Monomial meaning with examples

• Example 1: The expression 5x³ is a monomial. '5' is the coefficient, 'x' is the variable, and '3' is the exponent. This Monomial represents a single term, formed by multiplying the coefficient and the variable raised to a power. It can be evaluated by substituting values for 'x'.
• Example 2: The term '7y²z' represents a Monomial with a coefficient of 7, variables 'y' and 'z', and an implied exponent of 1 for 'z'. This single-term expression is formed through multiplication and exponentiation, making it a valid monomial. It does not include addition or subtraction signs.
• Example 3: The constant '10' is a Monomial because it can be written as 10x⁰. Here, 10 is the coefficient and x⁰ equals 1. This showcases how a single constant number aligns with the definition of a monomial. It adheres to the single-term criteria.
• Example 4: The expression 'x' itself is a monomial. It has an implied coefficient of 1 and an exponent of 1. It is a building block for creating other terms such as polynomials and other expressions. Its simplicity adheres with Monomial classification.
• Example 5: The term '-3a⁴b' is a Monomial, with coefficient of -3, variables 'a' and 'b' along with exponents '4' and '1'. It is a single term, formed using multiplication between numbers and variables raised to integer powers, meeting requirements of monomial.