The formula this page uses
degree = the largest exponent in the fully expanded, fully simplified polynomial
← Back to calculators
Degree Of Polynomial Calculator
Solve degree of polynomial problems with clear steps, notation, and a final check.
x²
Calculate without using AI.
Evaluate the governing formula locally in your browser. Define each known quantity once, then change values to test another case instantly.
Choose an example or enter a formula.
Show your work Step-by-step method
- No account, AI request, or paid token is used.
Recent calculations
No calculations yet.
Algebra
Degree Of Polynomial Calculator explained
The short version
- The degree is the biggest exponent left after you expand and simplify, not before.
- In a term with several letters, add the exponents: 4x²y³ has degree 5.
- Degree caps how many times the graph can cross the x-axis and how many bends it can have.
What each part means
SymbolWhat it means
n — DegreeThe highest power of the variable. A whole number, never a fraction or negative.
aₙ — Leading coefficientThe number in front of the highest-power term, including its sign.
a₀ — Constant termThe term with no variable. It is also the y-intercept.
terms — Number of terms1 is a monomial, 2 a binomial, 3 a trinomial. Separate from degree.
Show your work: a full example
- The expression3x²(2x³ − 5) + 4x⁵
- Multiply 3x² into the bracket6x⁵ − 15x² + 4x⁵
- Combine the two x⁵ terms10x⁵ − 15x²
- Find the biggest exponent5 beats 2, so the degree is 5
- Read the leading coefficient10, and it is positive
- Count the terms2 terms, so this is a binomial of degree 5
- Predict the graphodd degree with a positive lead, so it falls to the left and rises to the right, with at most 5 x-intercepts
A second, different case
- A different case: the top terms cancel(x³ + 2x) − (x³ − 7)
- Distribute the subtractionx³ + 2x − x³ + 7
- The cubes cancel0x³ + 2x + 7
- Simplify2x + 7, so the degree is 1, not 3
- A term with two letters4x²y³ has exponents 2 and 3
- Add them for that term's degree2 + 3 = 5
- Compare terms in 4x²y³ − x⁶degrees 5 and 6, so the polynomial's degree is 6
Copy-ready example
3x²(2x³ − 5) + 4x⁵
The expression
Questions about the Degree Of Polynomial Calculator
Does 1/x count as degree −1?
The exponent is −1, but that means the expression is not a polynomial at all. Polynomials allow only whole-number exponents of 0 or more, so 1/x is a rational function and questions about its degree are asking about something else.
Is √x a polynomial?
No. √x is x raised to the power ½, and a half is not a whole number. The same rule rules out x^1.5 and 2ˣ, where the variable sits in the exponent instead of the base.
Why does the degree limit how many roots there can be?
Every root corresponds to a linear factor, and multiplying n linear factors together produces exactly degree n. Fitting more than n factors would push the degree higher than the polynomial actually is.
What is the degree of the polynomial that is just 0?
It is left undefined, or written as −∞ in more advanced courses. Every other constant like 7 has degree 0, but 0 = 0x⁵ = 0x¹⁰⁰ equally well, so no single exponent can be singled out.