Answer
$f(x)=-2 (x+5)^2(x-4)(x-2)$
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:
$f(x)=k (x+5)^2(x-4)(x-2)~~~(1)$
Since, $(3,128)$ lies on the graph, we have:
$k(8)^2(-1)(1) =128 \\ -64k = 128 \\k=-2$
Thus, equation (1) becomes:
$f(x)=-2 (x+5)^2(x-4)(x-2)$
