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: November 11, 2024

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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 $4$ $4$ , $x^{2}$ $x^{2}$ , or $4x^{2}$ $4x^{2}$ . 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.
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.
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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Question

Is only a coefficient a monomial?

Iris8989

Community Answer

Yes, a coefficient with no variable in front of it is just a number. All numbers are monomials.

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What is the degree when there are no exponents?

Iris8989

Community Answer

When there are no exponents, the degree is one. You don't need to write the 1 with the term because everything raised to the power of one will equal itself. For example, 3^1 equals 3 (the same applies for variables and other numbers).

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Question

Classify the number of terms in 6x.

Iris8989

Community Answer

6x is one term. A term can consist of just a variable (like x or y), or a coefficient and a variable (like 4a or -2x). The coefficient and the variable are multiplied together. If there were more terms added together, you could classify it as a polynomial (like 4x + 6 or 3x^2 + 5x - 3).

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