Finding all complex roots of polynomial Given $\ i $ is a root for the polynom $\ p(x) = x^4 +2x^3 +3x^2 +2x +2  $ find all the roots of $\ p(x) $ in the $\ \mathbb C  $ field.
$\ x^4 + 2x^3 + 3x^2 + 2  \ /  \ x-i $
I get confused everytime I try to divide $\ p(x) $ by $\ x -i $. I end up with this residual: $\ 2+x^3i +2x^2i + 3xi +2i $

As the coefficients are real, when $a$ is a root so $\bar{a}$ is a root too. Then 
$$\dfrac{x^4 +2x^3 +3x^2 +2x +2}{x^2+1}=x^2+2x+2$$
