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Eisenstein_Criterion

Definition of Eisenstein Criterion :-

      Suppose F(x) = \(a_nx^n\) + \(a_{n-1}\) + -------------- + \(a_1x\) + \(a_0\)  is a polynomial with integer coefficients .

      Let 'p' be a prime number such that

                       1.    p divides each \(a_i\) for \(i \neq 0\)

                       2.   p does not divide \(a_n\), and

                       3.   \(p^2 \) does not divide \(a_0\)

      Then F(x) is irreducible over the rational number. It will also be irreducible over integers,  unless all its coefficients have a nontrivial factor in common.                          

2) Suppose that P is a prime number prove that \(


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