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The degree of a polynomial is defined as the greatest of the degrees of its terms. For example, the following is a polynomial of degree 5.
The monomial with the highest degree is 4xy^4. This means that the degree of the polynomial is 1+4=5. In other cases, if a polynomial consists of only a nonzero constant term, the polynomial has degree 0. For the special case of the zero polynomial, the degree is undefined. The following table summarizes this information by providing some specific examples.
| Polynomial | Degree |
|---|---|
| - 5 x^2y + x^2y^4 - 11x^2 - 3 | 6 |
| x - 11x^4 +8x^3 | 4 |
| 7 | 0 |
| 0 | Undefined |
Depending on the degree of a polynomial, it can have different characteristics. For example, a polynomial with degree 1 is linear, and a polynomial with degree 2 is quadratic.