If $f(x)$ is a polynomial of degree $4$ and $f(n)=n+1$ for $n=1,2,3,4$. Find $f(5)$ Question: If $f(x)$ is a polynomial of degree $4$ and $f(n)=n+1$ for $n=1,2,3,4$. Find $f(5)$ 
If we construct $g(x)=f(x)-(x-2)(x-3)(x-4)(x-5)$, then is it possible to find f(5)?

$f(x)=x+1+c(x-1)(x-2)(x-3)(x-4)$ satisfies the hypothesis for any $c \neq 0$. So it is not possible to find $f(5)$ from the given information. 
