A certain polynomial P(x) , $x\in R$ when divided by $x-a, x-b,x-c$ leaves the remainders a,b,c respectively. Find the remainder when P(x) is divided by $(x-a)(x-b)(x-c)$ is (a,b,c are distinct)
My approach : Remainder theorem : $\Rightarrow P(a) =a, P(b) =b; P(c) =c$
Now as per the question let the required remainder by R(x) , then $P(x) =(x-a)(x-b)(x-c) Q(x) +R(x) $
Where R(x) is a remainder of at most degree 2. Now from here I am not getting anything which helps me to solve this problems.. please help thanks..