What are the meanings of "monomial," "binomial" and "trinomial"?

A monomial, where “mono” means “one,” is a one-term polynomial. A binomial, with “bi” meaning “two,” is a polynomial with two terms. A polynomial with three terms is called a trinomial, as “tri” means “three.”

A monomial is a number, a variable, a number multiplied by a variable or a product of variables, where all of the exponents are nonnegative integers. It is one term of a polynomial. A polynomial is therefore composed of monomials combined by addition, subtraction, multiplication and division. Variables of a monomial can only have whole number exponents; thus, an expression with a variable in the denominator or a variable with a negative exponent is not a monomial. Some examples of monomials are 2, y, 3z, xy and 2mn.

Two monomials combined by addition or subtraction are called a binomial. Each binomial consists of two unlike terms, which means the two terms cannot be combined to be simplified. Examples of binomial are “2x + y” and “x² + x.”

A three-term polynomial, called a trinomial consists of three monomials separated by a plus or a minus sign. It consists of three unlike terms such as “x + y + z” and “x³ – x² + x.”