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)?

Note that, $f(x)=\lambda(x-1)(x-2)(x-3)(x-4)+x+1$. Here $\lambda$ is a non-zero scalar. Hence $f(5)=\lambda 4\cdot 3\cdot 2\cdot 1+6=6+24\lambda$.
