Enter Polynomial Data
Example Data Table
| Expression | Standard Form | Degree | Type | Leading Term |
|---|---|---|---|---|
| 4x^5 - 2x^3 + x - 7 | 4x^5 - 2x^3 + x - 7 | 5 | Quintic | 4x^5 |
| 7x^2 + 3x + 9 | 7x^2 + 3x + 9 | 2 | Quadratic | 7x^2 |
| -x^3 + 6x - 1 | -x^3 + 6x - 1 | 3 | Cubic | -x^3 |
| 12 | 12 | 0 | Constant | 12 |
| x^6 - 3x^6 + 5x^2 | -2x^6 + 5x^2 | 6 | 6th-degree polynomial | -2x^6 |
Formula Used
Degree of a polynomial:
Degree(P) = max(exponent of each non-zero term)
First write the expression in standard form, combine like terms, remove any term whose coefficient becomes zero, and then identify the largest remaining exponent.
Example: for 4x^5 - 2x^3 + x - 7, the exponents are 5, 3, 1, 0, so the degree is 5.
How to Use This Calculator
- Type a single-variable polynomial in expanded form.
- Enter the variable symbol used in the expression.
- Press Find Polynomial Degree.
- Read the degree, classification, and leading term above the form.
- Review the parsed term table to see how each exponent contributes.
- Use the CSV or PDF buttons to save your result summary.
- Check the Plotly graph to preview the polynomial’s behavior.
Frequently Asked Questions
1. What is the degree of a polynomial?
The degree is the largest exponent of the variable after the polynomial is simplified. Terms with zero coefficients do not count because they disappear from the final expression.
2. Does a constant have a degree?
Yes. Any non-zero constant has degree 0 because it can be viewed as a term multiplied by the variable raised to the zero power.
3. What about the zero polynomial?
The zero polynomial is a special case. Its degree is often called undefined because there is no non-zero term with an exponent to compare.
4. Why must exponents be non-negative integers?
That is part of the definition of a polynomial. Negative, fractional, or variable exponents create rational or algebraic expressions instead of standard polynomials.
5. Can this tool combine like terms?
Yes. If the same exponent appears more than once, the calculator adds the coefficients first, then finds the degree from the simplified result.
6. What is the leading term?
The leading term is the non-zero term with the highest exponent in standard form. Its coefficient is called the leading coefficient.
7. Can I use decimals in coefficients?
Yes. Decimal coefficients are allowed because polynomial coefficients can be real numbers. The restriction applies to exponents, not coefficients.
8. Why does the graph use a limited x-range?
High-degree polynomials can grow very quickly. A smaller adaptive range keeps the plotted curve readable and avoids extreme values that flatten the visual detail.