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.
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
2 years ago
Get the weekly newsletter! In it, you'll get:
see an example newsletter