Question 916833
But WHY is (0,0) also a factor?


I just answered this question a few minutes ago.


LOOK at the factorization of f(x).  You have the correct factorization.  Three separate factors written in x.
The list of factors:
x
(x+1)
(x-2)


Each of those gives a x-intercept.
Note that one of the factors is x, so this means that when x=0, f is also zero, BECAUSE x IS ONE OF THE FACTORS OF THE FUNCTION f.