Enter expanded polynomials and detect degree accurately today. Inspect leading terms, coefficients, variables, and structure. See summaries, exports, graphs, and examples in one place.
Degree of one term: deg(a·x^m y^n z^p) = m + n + p
Degree of a polynomial: deg(P) = max(deg(term₁), deg(term₂), ..., deg(termₖ))
Leading term: the nonzero term with the greatest degree after combining like terms.
Leading coefficient: the coefficient attached to the leading term.
Special cases: every nonzero constant has degree 0. The zero polynomial has no defined degree.
x^4 or a^2b^3.| Example expression | Simplified result | Degree | Leading term | Classification |
|---|---|---|---|---|
| 3x^4 - 2x + 7 | 3x^4 - 2x + 7 | 4 | 3x^4 | Quartic polynomial |
| 5a^2b^3 - 6ab + 1 | 5a^2b^3 - 6ab + 1 | 5 | 5a^2b^3 | Degree 5 polynomial |
| x^3 + 4x^3 - 2 | 5x^3 - 2 | 3 | 5x^3 | Cubic polynomial |
| 7 | 7 | 0 | 7 | Constant polynomial |
| x^2y + xy^2 + y | x^2y + xy^2 + y | 3 | x^2y | Cubic polynomial |
A valid input uses constants and variables with nonnegative integer exponents. Terms must be joined with plus or minus signs in expanded form.
Yes. The calculator supports multivariable expressions such as x^2y + 3xy^2 - 4. It adds exponents inside each term to get the term degree.
It first combines like terms, removes zero terms, computes every term degree, and then selects the largest remaining degree as the polynomial degree.
If all terms cancel, the result becomes the zero polynomial. In that case, the degree is shown as undefined because no nonzero term remains.
No. Negative exponents create rational expressions, not polynomials. Inputs like x^-2 or 1/x are rejected.
Yes. Coefficients such as 0.5x^3 and 2.75ab are accepted. The precision setting controls how numeric results are displayed.
If like terms combine or cancel, the highest surviving degree may change. That can alter the leading term and the displayed classification.
The graph compares simplified terms. Bars show each term degree, while the line trace shows each coefficient. It helps you inspect structure quickly.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.