Polynomials

In algebra, a cubic function is a function of the form where a is nonzero.

In algebra, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no algebraic solution—that is, solution in radicals—to the general polynomial equations of degree five or higher with arbitrary coefficients.

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

In algebra, the polynomial remainder theorem or little Bézout's theorem is an application of Euclidean division of polynomials.

In mathematics, a symmetric polynomial is a polynomial P(X1, X2, …, Xn) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial.

In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates with uniform scales) is a line in the plane.

In mathematics, Legendre functions are solutions to Legendre's differential equation: They are named after Adrien-Marie Legendre.

In mathematics, the symmetric algebra S(V) (also denoted Sym(V)) on a vector space V over a field K is the free commutative unital associative algebra over K containing V.

In mathematics, a polynomial matrix or sometimes matrix polynomial is a matrix whose elements are univariate or multivariate polynomials.

In mathematics, the determinant of a skew-symmetric matrix can always be written as the square of a polynomial in the matrix entries, a polynomial with integer coefficients that only depend on the size of the matrix.

In mathematics and computer algebra, factorization of polynomials or polynomial factorization is the process of expressing a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.

In knot theory, the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman.

In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials.

A polylogarithmic function in n is a polynomial in the logarithm of n, In computer science, polylogarithmic functions occur as the order of memory used by some algorithms (e.g., "it has polylogarithmic order").

The Touchard polynomials, studied by Jacques Touchard (), also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial type defined by where is a Stirling number of the second kind, i.

In algebra, the theory of equations is the analysis of the nature and algebraic solutions of algebraic equations (also called polynomial equations), which are equations defined by a polynomial.

In mathematics, Romanovski polynomials is an informal term for one of three finite subsets of real orthogonal polynomials discovered by Vsevolod Romanovsky (Romanovski in French transcription) within the context of probability distribution functions in statistics.

In mathematics, a matrix polynomial is a polynomial with matrices as variables.

In algebra, the content of a polynomial with integer coefficients (or, more generally, with coefficients in a unique factorization domain) is the greatest common divisor of its coefficients.

In algebra, an octic equation is an equation of the form where a ≠ 0.