Factor $x^3-x^2+2$ in $\mathbb Z_{3}[x]$ and explain why the factors are irreducible.
So the factor is supposed to be:
$x^3-x^2+2 = 2(x + 1)(2x^2 + 2x + 1)= (x + 1)(x^2 + x + 2)$.
But I don't really see how. What I see:
$x^3-x^2+2 \equiv x^3+2x^2+2$ in $\mathbb Z_{3}[x]$.
And I suppose it can factor to $x^2(x+2)+2$ ? I don't see where $2(x + 1)(2x^2 + 2x + 1)$ comes from.