If dividend = x4+x3−2x2+x+1, divisor = x - 1 and remainder = 2. Find the quotient q(x).
Given, x4+x3−2x2+x+1=(x−1)×q(x)+2
x3+2x2+1x−1 x4+x3−2x2+x−1x4−x3 –––––––––––––2 2x3−2x2+x−1 2x3−2x2––––––––––– x−1 x−1–––––– 0
∴q(x)=x3+2x2+1.