∵ Degree of numerator is greater than the degree of denominator. ∴ First we divide,
or =
2x4−x3+3x2−x+4
x2−3x+2
=(2x2+5x+14)+
31x−24
(x−2)(x−1)
...(i) Let
31x−24
(x−2(x−1)
=
A
x−1
+
B
x−2
⇒31−24=−A(x−2)+B(x−1) ...(ii) Put x=1 ⇒31−24=−A⇒A=−7 Put x=2 in Eq. (ii) 31×2−24=0+B⇒B=38 ∴ From Eq. (i) f(x)=2x2+5x+14 and A+B=−7+38=31