I need some help understanding the following worked example:

So they have $\displaystyle \alpha = x +I$ where I = <p(x)>. But what do they mean "by long division we have..."? Did they divide p(x) by $\displaystyle \alpha$? If so how could they end up with $\displaystyle (x-\alpha) (x+2+\alpha)$? Any help is really appreciated.