### Polynomial

An expression

is called a polynomial with variable over field ,

where (and ). Number is the degree of the polynomial, and the set of all polynomials with coefficients in is denoted by . Two polynomials can be added or multiplied in a natural way.

Every polynomial is related to the polynomial function associating with the value of the polynomial for .

### Roots of polynomials

An element is called a root of polynomial , if .

The field is algebraically closed, if every polynomial over has a root. The Fundamental Theorem of Algebra states that field is algebraically closed.

If is a polynomial of degree and is its root, then for a polynomial of degree .