# Polynomial

A **polynomial** in one variable is a function of the form:

In elementary mathematics, the coefficients are typically chosen to be real or complex numbers. However, it makes sense to define a polynomial with coefficients in any ring.

The largest power of that appears in the polynomial is called the degree of the polynomial.

- Example: is a degree 3 polynomial with integer coefficients.

A polynomial in two variables is, similarly, a finite sum

, where the coefficients are elements of some ring. Polynomials in 3 or more variables are defined similarly.

When we substitute a value *b* into the polynomial *f(x)* then we get an actual number as output. This number is the value . This process is called "evaluating the polynomial at *b*".

Some algorithms are said to perform in polynomial time. There are algorithms which can factor polynomials in an amount of time that is a polynomial n^{k}.