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