Polynomial $f(x)$ degree problem. Suppose the polynomial $f(x)$ is of degree $3$ and satisfies $f(3)=2$, $f(4)=4$, $f(5)=-3$, and $f(6)=8$. Determine the value of $f(0)$.
How would I solve this problem?  It seems quite complicated...

Let 
$$L_3(x)=\frac{(x-4)(x-5)(x-6)}{(3-4)(3-5)(3-6)}$$
so notice that $L_3(3)=1$ and $L_3(k)=0$ for $k=4,5$ or  $6$ and define by the same way $L_4, L_5$ and $L_6$
so we see that
$$f(x)=f(3)L_3(x)+f(4)L_4(x)+f(5)L_5(x)+f(6)L_6(x)$$
and now the calculus of $f(0)$ isn't hard.
