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 $f(0)$.

We have the following system of equations

27a  + 9b  +  3c  + d   =   2

64a  +16b  +  4c  + d  =   4

125a  + 25b  + 5c + d  = -3

216a  + 36b  +  6c  + d  = 8

Soving this isn't difficult, but it is tedious

Using  a CAS we have that

a = 9/2, b = -117/2, c = 245, d = -328 

f (0)  =  d   =   -328