In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers – ...
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Eisenstein's Irreducibility Criterion ... be a polynomial with integer coefficients. Suppose a prime p divides each of a 0 , a 1 , . . . , a n − 1 (every ...
Eisenstein's irreducibility criterion is a method for proving that a polynomial with integer coefficients is irreducible (that is, cannot be written as a ...
Eisenstein's irreducibility criterion is a sufficient condition assuring that an integer polynomial p(x) is irreducible in the polynomial ring Q[x].
Duration: 3:50
Posted: May 2, 2023
Posted: May 2, 2023
This article explores the history of the Eisenstein irreducibility criterion and ex- plains how Theodor Schönemann discovered this criterion before Eisenstein.
Let $a_0, a_1, ... ,a_n$ be integers. Then, Eisenstein's Criterion states that the polynomial $a_nx^n+a_{n-1}x^{n- cannot be factored into the product of ...