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...

If you just want to use subtraction, you could take first differences 
               2   4  -3   8 
                 2  -7  11
                  -9  18
                    27

then expand this to the left
-328 -137 -36  2   4  -3   8 
   191  101  38  2  -7  11
     -90 -63 -36  -9  18
        27  27  27  27

