I believe MKLyon was talking about these -1s. He is correct that there is a typo. The lines should read:
which shows that the polynomial IS reducible in Z3[x].
(Okay, so the red coloring didn't work in the quote! You still get the idea.)
-Dan
PS: That x = 1 produces
implies that x - 1 is a factor of the polynomial in Z3[x]. By doing the long division you can show that
. Where is the x + 2 factor in the above list? Well, this would imply a root of x = -2 = 1 (mod 3), so really x = 1 again. This says that:
in Z3[x].