Galois group of x^4-2x^3-8x-3

[@juliefinkjulesheartmagic1111]

Great video!

[@arekkrolak6320]

Hey, you can choose any finite field to prove polynomial irreducable or you need to guess 5?

[@Seven-7-77]

Yes I think you can.

[@coconutmath4928]

If you choose F_2 the polynomial becomes x^4+1, which is reducible because it has 1 as a root, so you do have to go slightly further to F_5. (F_3 doesn't work either)

[@zachteitler9622]

Very nice. Another way to check that h is irreducible is with the Rational Root Theorem (en.wikipedia.org/wiki/Rational_root_theorem ).

[@grumpyparsnip]

I came here to say this.

[@coconutmath4928]

Yep, people always seem to forget about that theorem but you can definitely use it, I think I even used it in another video haha.