Eisenstein's criterion
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High Quality Content by WIKIPEDIA articles! In mathematics, Eisenstein's criterion gives sufficient conditions for a polynomial with integer coefficients to be irreducible over the rational numbers (or equivalently, over the integers; see Gauss's lemma).Suppose we have the following polynomial with integer coefficients.f(x)=a_nx^n+a_{n-1}x^{n-1}+cdots+a_1x+a_0.,If there exists a prime number p such that the following three conditionals all apply: p divides each ai for i n, p does not divide an, and p2 does not divide a0,then f(x) is irreducible over the rationals.

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High Quality Content by WIKIPEDIA articles! In mathematics, Eisenstein's criterion gives sufficient conditions for a polynomial with integer coefficients to be irreducible over the rational numbers (or equivalently, over the integers; see Gauss's lemma).Suppose we have the following polynomial with integer coefficients.f(x)=a_nx^n+a_{n-1}x^{n-1}+cdots+a_1x+a_0.,If there exists a prime number p such that the following three conditionals all apply: p divides each ai for i n, p does not divide an, and p2 does not divide a0,then f(x) is irreducible over the rationals.