# Polynomial

### From Conservapedia

A **polynomial** in one variable *x* is a function *f*(*x*) of the form:

*f*(*x*) = *a*_{n}*x*^{n} + *a*_{n − 1}*x*^{n − 1} + ... + *a*_{2}*x*^{2} + *a*_{1}*x* + *a*_{0}

In elementary mathematics, the coefficients *a*_{i} 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 *x* that appears in the polynomial is called the degree of the polynomial.

- Example:
*f*(*x*) = 4*x*^{3}− 3*x*+ 1 is a degree 3 polynomial with integer coefficients.

A polynomial in two variables *x*,*y* is, similarly, a finite sum

,
where the coefficients *a*_{ij} 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 *a*_{n}*b*^{n} + *a*_{n − 1}*b*^{n − 1} + ... + *a*_{2}*b*^{2} + *a*_{1}*b* + *a*_{0}. 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}.