Let the remainder, when p(x) is divided by x2−5x+6 be ax+b b and quotient be q(x) by division algorithm. p(x)=(x2−5x+6)q(x)+ax+b =(x−2)(x−3)q(x)+ax+b Given p(2)=6;p(3)=4 p(2)=2a+b⇒2a+b=6→ (1) p(3)=3a+b⇒3a+b=4 → (2) Solving (1) and (2), a=−2;b=10 ∴ Required remainder =−2x+10