Answer
$f(x)=x^3 (x+4)(x-2)$
Work Step by Step
Let us consider that $a$ is a zero of a function with multiplicity $b$. Then this factor of the function can be expressed as: $(x-a)^b$.
Therefore, we can write the equation of the function as:
$f(x)=k x^3 (x+4)(x-2)~~~~~(1)$
Since, $(-2, 64)$ lies on the graph, we have:
$k(-2)^3(2)(-4) =64 \\ 64k = 64 \\k=1$
Thus, equation (1) becomes:
$f(x)=x^3 (x+4)(x-2)$
