Degree of Polynomial Calculator

Enter Polynomial

Use +, -, *, variables, and powers like x^5 or a^2b^3.

Accepted Formats

x^5 + 2x^2 - 1

3a^2b^4 - 7ab + 9

4m*n^3 + 2

For multivariable terms, the term degree is the sum of exponents. The polynomial degree is the largest non-zero term degree.

What This Calculates

Highest term degree
Term-by-term exponent analysis
Polynomial classification
Variable type detection
CSV and PDF export support

Formula Used

Single-variable term: If a term is written as axⁿ, its degree is n.

Multivariable term: If a term is written as a x^p y^q z^r, its degree is p + q + r.

Polynomial degree: Degree of polynomial = maximum degree among all non-zero terms.

Examples: Degree of 6x⁵ is 5. Degree of 3a²b⁴ is 6. Degree of 8 is 0.

How to Use This Calculator

Enter a polynomial expression in the input box.
Use exponent notation such as x^3 or a^2b^4.
Click Calculate Degree.
Review the result summary shown above the form.
Check the term analysis table for exponent details.
Download CSV or PDF if you need a record.

Example Data Table

Polynomial	Highest-Degree Term	Degree	Classification
7x^4 - 2x + 9	7x^4	4	Quartic polynomial
3a^2b^5 + 6ab - 1	3a^2b^5	7	Degree 7 polynomial
5x - 8	5x	1	Linear polynomial
12	12	0	Constant polynomial
0	None	Undefined	Zero polynomial

FAQs

1. What does polynomial degree mean?

It is the highest degree among all non-zero terms in the polynomial. For one variable, degree is the largest exponent. For several variables, add exponents within a term first.

2. How is degree found for multivariable terms?

Add the exponents in the same term. For example, a^2b^3 has degree 5 because 2 + 3 = 5. Then compare that with other non-zero terms.

3. What is the degree of a constant?

Any non-zero constant has degree 0 because it has no variable factor. Examples include 4, -19, and 2.75.

4. What is the degree of the zero polynomial?

The zero polynomial is usually treated as having undefined degree. This calculator labels it undefined because no non-zero term exists to establish a highest degree.

5. Can coefficients change the degree?

No. Coefficients affect magnitude, not degree, unless a coefficient makes a term zero. Degree depends on the variable exponents of non-zero terms.

6. Does term order matter?

No. You can write the polynomial in descending order, ascending order, or mixed order. The calculator still searches all non-zero terms and finds the maximum degree.

7. Can this handle expressions with several variables?

Yes. It analyzes variables and exponents term by term. For multivariable expressions, each term degree is the sum of its exponents.

8. Why export results as CSV or PDF?

Exports are useful for homework records, reports, teaching notes, and checking multiple examples. CSV helps with spreadsheets, while PDF is convenient for sharing or printing.