Degree of a Polynomial
High School
Definition
Refers to the highest degree in a polynomial. The degree in an expression tells us the order of an equation. They are represented by small numbers above and slightly beside a variable telling you that variable is raised to a certain degree.
Worked examples
\(5x^3 + 2x^2 - 7x + 1\)
The highest exponent is 3, so the degree of this polynomial is 3.
\(4x^5 - x^3 + 9x^4 - 2\)
Even though terms aren't in order, the highest exponent is 5, making this degree 5.
\(7x - 3\)
The highest exponent on x is 1, so this linear polynomial has degree 1.
Common mistakes
- \(3x^2 + 5x^4 - 1\) has degree 2 → \(3x^2 + 5x^4 - 1\) has degree 4 The degree is the largest exponent in the entire polynomial, not the first term's exponent.
- \(2x^3 + 4x^2\) has degree 5 → \(2x^3 + 4x^2\) has degree 3 Don't add the exponents together — just find the single highest one.
- \(6x^3\) has degree 18 → \(6x^3\) has degree 3 The coefficient doesn't affect degree; only the exponent on the variable counts.
Where you'll use it next
You'll use degree to classify polynomials, predict the number of roots and turning points when graphing, and determine end behavior in precalculus and calculus.
Found in 2 StudyPug lessons
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.
Understanding Polynomial Functions: From Basics to Applications
12th Grade12thGrade 12 Math
Explore polynomial functions, their key components, and real-world uses. Learn to identify, analyze, and solve polynomial equations with confidence. Boost your algebra skills and prepare for advanced math concepts.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026