hi ia am having a lil problem with this q

$\displaystyle f(x)=x^{3}-x^{2} + 1 and g(x)=x^{2} - 4$

what is the gcd over Q[x] and $\displaystyle F_{5}[x]$

for Q[x] i get $\displaystyle f_{1}=f-xg=-x^{2}+4x+1$

therefore $\displaystyle f_{2}=f_{1} +g =4x-3 $

=> giving me $\displaystyle f=f_{1}+xg=f_{2}-g+xg=(x-1)g+(4x-3) $

i think i have got ferther and i get and answer of gcd -33/16

Now im stuck

thanks Bobisback