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# Monomials, Binomials and Polynomials

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When dealing with differing kinds of Polynomials, there are several varieties. Today we will explore a few different variations, and break down the simple formula for naming them.

A monomial is the product of non-negative powers of variables. A monomial has no variables in its denominator and will only have one term.

For example: 13, 3x, -57, x², 4y², or -2xy

A binomial is the sum of two monomials and thus will have two unlike terms.

For example: 3x + 1, x² – 4x, 2x + y, or y – y²

A trinomial is the sum of three monomials, meaning it will be the sum of three unlike terms.

For example: x² + 2x + 1, 3x² + 4x – 10, 2x + 3y + 2

A polynomial is the sum of one or more terms.

For example: x² + 2x, 3x³ + x² + 5x + 6, 4x – 6y + 8

A good clue when trying to remember the meaning of these terms is the prefix on each word. In the word monomial, the prefix “mono” means one. In the word binomial, the prefix “bi” implies two. In the word trinomial, the prefix “tri” means three and in the word polynomial, the prefix “poly” means many.

Polynomials are in simplest form when they contain no similar terms. Similar terms are terms in the polynomial which are raised to the same power. For example, in the polynomial, 4x² + 4x – 3 + 3x², the terms 4x² and 3x² are similar terms. The simplified form of 4x² + 4x – 3 + 3x² is 7x² + 4x – 3. Another example of simplifying a polynomial would be: x² +2x +1 + 3x² – 4x is simplified to 4x² – 2x + 1.

Polynomials are generally written in descending order. For example the polynomial 4x² – 2x + 1 is written in descending order. In order for a polynomial to be in descending order the exponents of the variables decrease from left to right.

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