# Definition:Degree of Polynomial/Field

## Definition

Let $\left({F, +, \times}\right)$ be a field whose zero is $0_F$.

Let $\left({K, +, \times}\right)$ be a subfield of $F$.

Let $x \in F$.

Let $\displaystyle f = \sum_{j \mathop = 0}^n \left({a_j x^j}\right) = a_0 + a_1 x + \cdots + a_n x^n$ be a polynomial over $K$ in $x$ such that $a_n \ne 0$.

Then the **degree of $f$** is $n$.

The **degree of $f$** can be denoted $\deg \left({f}\right)$ or $\partial f$.

## Also known as

The **degree** of a polynomial is also referred to by some sources as its **order**.

## Sources

- 1964: Murray R. Spiegel:
*Theory and Problems of Complex Variables*... (previous) ... (next): $1$: Complex Numbers: Polynomial Equations