Prove that the polynomial $3x^5-12x^4+21x^3-9x+2$ is irreducible over the rationals
$p=2: f(x)=x^5+x^3+x$..this has root..So this is not irreducible over $Z_2$
so Can I conclude $f(x)$ is irreducible over the rationals?
Try Eisenstein's criterion on $x^5 P(1/x)$.
Hint: Try $p=3$ instead. Remember to appeal to Gauss's lemma at some point.
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1 year ago