If x-3 is a factor of f(x), then f(3) = 0. We can use synthetic division to verify this:
3 | 1 -1 -5 -3
| 3 6 3
|-------------
| 1 2 1 0
The result of the synthetic division is 1x^2 + 2x + 1, which can be factored as (x+1)(x+1). Therefore, the zeros of f(x) are:
f(x) = 0 if x = 3, -1, -1
So the zeros of the function f(x) are 3, -1, and -1.