GCD polynomials

hi ia am having a lil problem with this q

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

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

for Q[x] i get $f_{1}=f-xg=-x^{2}+4x+1$
therefore $f_{2}=f_{1} +g =4x-3$
=> giving me $f=f_{1}+xg=f_{2}-g+xg=(x-1)g+(4x-3)$

i think i have got ferther and i get and answer of gcd -33/16
Now im stuck
thanks Bobisback