Shifted Eisenstein polynomial
= Shifted Eisenstein polynomial
{title2=$f(T+a)$}
A <polynomial> may fail the <Eisenstein polynomial> test while a translate $f(T+a)$ passes it. Translation does not change the generated extension: if $f(\alpha)=0$, then $f(T+a)$ vanishes at $\alpha-a$. For $f(T)=T^3-m$, the translate by $m$ is Eisenstein at $3$ whenever $3\nmid m$ and $m\not\equiv\pm1\pmod9$.