# How to find the splitting field for $x^3-x^2-x-2$ over $\Bbb Q$? [closed]

I'm not quite sure on how to solve this one. Any help would be appreciated. :)

## closed as off-topic by Alex Provost, YiFan, Leucippus, Eevee Trainer, GNUSupporter 8964民主女神 地下教會Mar 24 at 23:30

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Hint: This polynomial has a rational root. Actually, it factors as $$x^3-x^2-x-2=(x-2)(x^2+x+1),$$ so it is the splitting field of the quadratic polynomial $$x^2+x+1$$, which I'm sure you've already met.