Eisenstein Criterion

Eisenstein's Criterion is a method used in algebra to determine whether a polynomial with integer coefficients is *irreducible*, meaning it cannot be factored into simpler polynomials with integer coefficients. The criterion states that if there's a prime number \( p \) such that: (1) \( p \) divides all coefficients except the leading one, (2) \( p \) does not divide the leading coefficient, and (3) \( p^2 \) does not divide the constant term, then the polynomial cannot be factored over the integers. This provides a straightforward way to test the irreducibility of many polynomials.