Degree of a term
High School
Definition
The exponent of a term. For example \(3x^6\), the degree will be 6. For multiple variables within the same term, the degree is the sum of all the variables exponents. For example \(3x^5y^4\), the degree will be 9. In the case of a polynomial with multiple terms, the degree of the polynomial is the highest degree of any term. For example \(4x^3 + 2x^2 + 5\), the degree of the polynomial is 3, because it is the highest.
Worked examples
\(7x^4\) has degree 4
The exponent on the variable is the degree of the term.
\(3x^5y^4\) has degree \(5 + 4 = 9\)
With multiple variables, add all the exponents together to find the degree.
\(4x^3 + 2x^2 + 5\) has degree 3
The polynomial's degree is the highest degree among its terms; \(4x^3\) has degree 3.
Common mistakes
- \(3x^5y^4\) has degree 5 → \(3x^5y^4\) has degree 9 You must add all variable exponents: \(5 + 4 = 9\).
- \(7x^4\) has degree 7 → \(7x^4\) has degree 4 The coefficient is not part of the degree; only the exponent counts.
- \(4x^3 + 2x^5 + 1\) has degree 3 → \(4x^3 + 2x^5 + 1\) has degree 5 The polynomial's degree is the highest degree of any term, so it is 5, not 3.
Where you'll use it next
You'll use degree to classify polynomials, predict graph behavior, apply the remainder and factor theorems, and choose techniques for polynomial division and integration in calculus.
Found in 1 StudyPug lesson
Understanding Polynomial Components: A Comprehensive Guide
10th Grade10thGrade 10 Math
Dive into the world of polynomials! Learn to identify terms, coefficients, and degrees. Master standard form and leading terms. Boost your algebra skills with our in-depth guide to polynomial components.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026