A monomial is an algebraic expression consisting of a single term. It is written as the product of a numerical coefficient and one or more variables, each raised to a non-negative integer exponent.

A binomial refers to a polynomial that contains exactly two non-zero terms. Its general form is expressed as ( a + b ) or ( a - b ).

A trinomial is defined as a polynomial consisting of exactly three non-zero, pairwise distinct terms. More generally, within a commutative ring with unity, a trinomial in the indeterminate x is any...

Let R be a commutative ring and R [ x ] the ring of polynomials in one indeterminate over R. Consider two polynomials P ( x ) and Q (

Let P ( x ) and D ( x ) be polynomials in \mathbb{R} [ x ] with D ( x ) \neq 0.

The synthetic division (or Ruffini’s rule) is a method for dividing a polynomial by a binomial of the form ( x - a ).

Let p ( x ) be a polynomial with coefficients in a field \mathbb{F}, typically \mathbb{R} or \mathbb{C}. A root or zero of p is any element r \in \mathbb{F} such that

The binomial theorem asserts that for any positive integer n, the expression ( a + b )^{n} can be expanded as a finite sum of n + 1 terms.

Notable products are identities describing the expansion or factorisation of polynomials such as binomials or trinomials.

Partial fraction decomposition is a practical and widely used method for rewriting a rational function (a quotient of two polynomials) as a sum of simpler elementary fractions.