factorability
Factorability is the property of an algebraic expression to be written as a product of nontrivial factors within a specified algebraic structure, such as a ring or field. In the context of polynomials, a polynomial is factorable if it can be expressed as a product of polynomials of smaller positive degree with coefficients in the same coefficient domain; it is irreducible if no such nontrivial factorization exists. Factorability depends on the chosen domain, since a polynomial may factor over one ring but be irreducible over another. For example, x^2 − 5x + 6 factors over the integers as (x − 2)(x − 3), and hence over the rationals as well; x^2 + 1 is irreducible over the real numbers and over the rationals.
Gauss's lemma shows that, for polynomials with integer coefficients, factorization in Z[x] corresponds to factorization in
Common methods for testing and finding factors include the rational root theorem, factoring by grouping, and
Factorability also contrasts with integer factorization, the decomposition of integers into primes, and with broader notions