The quotient q(x) is
x3+2x2+1(x−1)x4+x3−2x2+x−1 x4−x3 − +–––––––––––––––2 2x3−2x2+x−1 2x3−2x2 − +–––––––––––––––– x−1 x−1− +–––––– 0 –––––
So, q(x)=x3+2x2+1