Let the quotient, when x3−6x2+ax+b is divisible by (x2−3x+2) be x−p. ⇒ (x2−3x+2)(x−p)=x3−6x2+ax+b ⇒ x3−3x2+2x−px2+3px−2p =x3−6x2+ax+b ⇒ x3−(3+p)x2+(2+3p)x−2p =x3−6x2+ax+b On comparing both sides, −(3+p)=−6 ⇒ p=6−3=3 2+3p=a⇒2+3×3=a⇒a=11 and −2p=b⇒−2×3=b⇒b=−6