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Irreducible polynomial - Wikipedia

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In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility depends on the nature of the coefficients that are accepted for the possible factors, that is, the ring to which the coefficients of the polynomial and its possible factors are supposed to belong. For example, the polynomial x2 − 2 is a polynomial with integer coefficients, but, as every integer is also a real number, it is also a polynomial with real coefficients. It is irreducible if it is considered as a polynomial with integer coefficients, but it factors as ( 𝑥 − 2 ) ( 𝑥 + 2 ) if it is considered as a polynomial with real coefficients. One says that the polynomial x2 − 2 is irreducible over the integers but not over the reals. Polynomial irreducibility can be considered for polynomials with coefficients in an integral domain, and there are two common definitions. Most often, a polynomial over an in

Irreducible polynomial - Wikipedia Jump to content From Wikipedia, the free encyclopedia Polynomial without nontrivial factorization This article is about non-factorizable polynomials. For polynomials which are not a composition of polynomials, see Indecomposable polynomial . This article includes a list of general references but lacks corresponding inline citations . Please help improve this article by introducing more precise citations. ( March 2015 ) ( Learn how and when to remove this message ) In mathematics , an irreducible polynomial is, roughly speaking, a polynomial that cannot be fac

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