Irreducible Polynomial
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High Quality Content by WIKIPEDIA articles! In mathematics, the adjective irreducible means that an object cannot be expressed as the product of two or more non-trivial factors in a given set. See also factorization. For any field F, the ring of polynomials with coefficients in F is denoted by F[x]. A polynomial p(x) in F[x] is called irreducible over F if it is non-constant and cannot be represented as the product of two or more non-constant polynomials from F[x]. The property of irreducibility depends on the field F; a polynomial may be irreducible over some fields but reducible over others....
High Quality Content by WIKIPEDIA articles! In mathematics, the adjective irreducible means that an object cannot be expressed as the product of two or more non-trivial factors in a given set. See also factorization. For any field F, the ring of polynomials with coefficients in F is denoted by F[x]. A polynomial p(x) in F[x] is called irreducible over F if it is non-constant and cannot be represented as the product of two or more non-constant polynomials from F[x]. The property of irreducibility depends on the field F; a polynomial may be irreducible over some fields but reducible over others. Some simple examples are discussed below. Galois theory studies the relationship between a field, its Galois group, and its irreducible polynomials in depth. Interesting and non-trivial applications can be found in the study of finite fields.
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