How to Classify Polynomials: By Type or Degree

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Identify polynomials by number of terms

Co-authored by Kyle Smith Reviewed by Joseph Meyer

Last Updated: September 27, 2023 Fact Checked

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Classify by Terms

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Classify by Degree

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Trying to classify a polynomial for Algebra homework? You’re in the right place! A polynomial is a math expression that adds terms with one or more variables and coefficients. Polynomials can be classified by the number of terms or the degree. This wikiHow guide shows you how to classify polynomials.

Things You Should Know

A term is a coefficient, variable, or both.
Monomials have 1 term. Binomials have 2 terms. Trinomials have 3 terms.
Classify by degree by identifying the highest exponent in the polynomial.

Method 1

Method 1 of 2:

Classify by Terms

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1
Identify the number of terms. A term consists of a coefficient, variable, or both. For example, you could have $4$ , $x^{2}$ , or $4x^{2}$ . You can use the number of terms to determine the type of polynomial you’re dealing with.
- Monomials have 1 term.
- Binomials have 2 terms.
- Trinomials have 3 terms.
- Polynomials with more than 3 terms are usually just identified by their degree.
- The variables should have non-negative integer exponents.
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2
Check out these examples.
- $2x$ is a monomial.
- $7$ is also a monomial, since it can be written as $7x^{0}$
- $3x+1$ is a binomial.
- $x^{5}+2x^{2}+x$ is a trinomial.

Method 2

Method 2 of 2:

Classify by Degree

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1
Identify the degree. The degree of a polynomial is the largest exponent present in a term.
- The standard form is when a polynomial’s terms are arranged in descending order of exponent size.
- For factoring info, check out our guide on factoring a cubic polynomial .
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2
See these examples from the last method:
- $2x$ is a 1st degree polynomial.
- $7$ is a zeroth degree polynomial, since it can be written as $7x^{0}$ .
- $3x+1$ is a 1st degree polynomial.
- $x^{5}+2x^{2}+x$ is a 5th degree polynomial.

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How would you classify: 2x^2+7?

Community Answer

That is a second-degree binomial, as the highest power is two and there are two terms.

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What is the degree and polynomial of 18x²-12x+5?

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That is a second-degree trinomial, because its highest exponent is2, and it has three terms.

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What is the degree of -2x^3+5x+8?

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Third degree (the highest power is three).

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For more polynomial math, see our guides on solving polynomials and multiplying polynomials.

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Check out another cool Algebra guide: How to Algebraically Find the Intersection of Two Lines .

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How to Classify Polynomials: By Type or Degree

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Classify by Terms

Classify by Degree

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