F(x) is a polynomial whose degree is atleast 3. When it is divided by x-5, the remainder is 17. When F(x) is divided by x-6, the remainder is 19. Find the remainder when F(x) is divided by (x-5) (x-6).

dividend = d*q+remainder f(x)=(x-5)q1+17 f(5)=0+17 f(x)=(x-6)q2+19 f(6)=0+19 let ax+b be the remainder when divided by (x-5)(x-6) f(x)=(x-5)(X-6)q3+ax+b f(5)=0+5a+b f(6)=0+6a+b f(5)=17=5a+b f(6)=19=6a+b subtract a=2 b=7 remainder=2x+7