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Finding the Degree of Polynomials

Example

Example of Classifying Polynomials and Finding Their Degrees

To determine the type and degree of a polynomial, count its terms to classify it, find the degree of each term, and identify the highest degree among the terms. For example:

$7y^2 - 5y + 3$ : This has $3$ terms, making it a trinomial. The degrees of its terms are $2$ , $1$ , and $0$ . The highest degree is $2$ , so the degree of the polynomial is $2$ .
$-2a^4b^2$ : This has $1$ term, making it a monomial. The degree of its single term is $4 + 2 = 6$ , so the degree of the polynomial is $6$ .
$3x^5 - 4x^3 - 6x^2 + x - 8$ : This has $5$ terms, making it a polynomial (with no special name). The degrees of its terms are $5$ , $3$ , $2$ , $1$ , and $0$ . The highest degree is $5$ , so the degree of the polynomial is $5$ .
$2y - 8xy^3$ : This has $2$ terms, making it a binomial. The degrees of its terms are $1$ and $1 + 3 = 4$ . The highest degree is $4$ , so the degree of the polynomial is $4$ .
$15$ : This has $1$ term, making it a monomial. As a constant, the degree of its single term is $0$ , so the degree of the polynomial is $0$ .

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Updated 2026-04-29

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OpenStax Intermediate Algebra

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