IS f(x)= x^4 + x^3 -x^2 - 2x -2 irreducable over Q??
Ive shown that this has no linear factors as +-1 +-2 are not roots.
Then I let F(x)=(x^2+ax+b)(x^2+cx+d)
And I end up with
But i can seam to show why no a b c d exist (or Exist)
Is there an easier approach?
I have an exam in 12 hours so I hope soeone can help!
Thanks in advance!