Polynomials in one variable x are algebraic expressions of the form

P(x) = c₀ + c₁x + c₂x² + c₃x³ + ... + c_Nx^N.

Here c₀, c₁, c₂, ... c_N are called the coefficients of the polynomial. If c_N 0 then the degree of this polynomial is the nonnegative integer N. A polynomial in one variable can also be conveniently expressed using the summation notation as

Then a polynomial in two variables x and y is an algebraic expression of the form

Polynomials in three or more variables are defined in a similar manner. In general the coefficients of a polynomial can belong to an arbitrary commutative ring. But in this article we will restrict our attention to polynomials in one variable and with coefficients in the field of complex numbers C, or in a familiar subring of this field. For more information on polynomials in two or...