Polynomial decomposition

In mathematics, a polynomial decomposition expresses a polynomial f as the functional composition ${\displaystyle g\circ h}$ of polynomials g and h, where g and h have degree greater than 1; it is an algebraic functional decomposition. Algorithms are known for decomposing univariate polynomials in polynomial time.

Polynomials which are decomposable in this way are composite polynomials; those which are not are indecomposable polynomials or sometimes prime polynomials^[1] (not to be confused with irreducible polynomials, which cannot be factored into products of polynomials). The degree of a composite polynomial is always a composite number, the product of the degrees of the composed polynomials.

The rest of this article discusses only univariate polynomials; algorithms also exist for multivariate polynomials of arbitrary degree.^[2]