*n*has the following form:

*a _{n}x^{n}* +

*a*

_{n}_{-1}

*x*

^{n}^{-1}+ ... +

*a*

_{2}

*x*

^{2}+

*a*

_{1}

*x*

^{1}+

*a*

_{0}

*x*

^{0}

where the *a*'s represent the coefficients and *x* represents the variable. Because *x*^{1} = *x* and *x*^{0} = 1 for all *x*, the above expression can be simplified to:

*a _{n}x^{n}* +

*a*

_{n}_{-1}

*x*

^{n}^{-1}+ ... +

*a*

_{2}

*x*

^{2}+

*a*

_{1}

*x*+

*a*

_{0}

When an *n*th-degree univariate polynomial is equal to zero, the result is a univariate polynomial equation of degree *n*:

*a _{n}x^{n}* +

*a*

_{n}_{-1}

*x*

^{n}^{-1}+ ... +

*a*

_{2}

*x*

^{2}+

*a*

_{1}

*x*+

*a*

_{0}= 0

There may be several different values of *x*, called roots, that satisfy a univariate polynomial equation. In general, the higher the order of the equation (that is, the larger the value of *n*), the more roots there are.

A univariate polynomial equation of degree 1 (*n* = 1) constitutes a linear equation. When *n* = 2, it is a quadratic equation; when *n* = 3, it is a cubic equation; when *n* = 4, it is a quartic equation; when *n* = 5, it is a quintic equation. The larger the value of *n*, the more difficult it is to find all the roots of a univariate polynomial equation.

Some polynomials have two, three, or more variables. A two-variable polynomial is called bivariate; a three-variable polynomial is called trivariate.