Concept

Polynomial

A polynomial is either a single monomial or a sum of them. Each of the monomials that form the polynomial are referred to as a term of the polynomial. This definition implies that, for an expression to be a polynomial, each of its terms must be a valid monomial.

Example Polynomial ✓ 5 x y + 2 x y^{2} + 8 x - 9 Not a Polynomial \times 3 x y + 2 x y^{- 2} + 7 x y^{3} - 1

In the above example, the latter expression is not a polynomial because the term

2 x y^{- 2}

is not a monomial. The variables in a monomial can only have whole numbers as exponents.

Classifying Polynomials by Their Number of Terms

One way that polynomials can be classified is according to the number of terms they have. The following table shows the names used for this classification.

Name	Definition	Example
Monomial	A polynomial with a single term.	$3 x^{2} y^{3}$
Binomial	A polynomial with a exactly two terms.	$5 x y + 3 x^{2} y^{3}$
Trinomial	A polynomial with exactly three terms.	$x^{3} - 9 x + 4$

When there are more than three terms, the name polynomial is commonly used.

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Classifying Polynomials by Their Number of Terms