So according to WolframAlpha the answer should be $1$ (And by inspection it certainly looks like it should be $1$.

My current working using Euclidean algorithm and polynomial long division

$x^3-x^2+2) = (x) \times (x^2-x+1) + (2-x)$  

$x^2-x+1 = (-1-x) \times (2-x) + 3$  

$(2-x) = \frac{2}{3} \times 3 - x$

Ok not sure what's going on now - I could keep going but I don't see it ever reaching $1$ 

What have I done wrong here?