Negligible function defined as product of polynomial and a negligible function How do I prove that a function $f_2$, defined as the product of a negligible function $f_1$ and a polynomial $p$, is itself negligible? 

$$f_2(n)= p_1(n)f_1(n)$$  

I see $f_2$ as negligible simply because I know that if you have something that has a negligible probability of happening $(f_1)$ then if you try a polynomial number of times $(p)$ we are still left with a negligible result. But I do not know how to prove this. I would appreciate if someone could point me in the right direction.

I have had a look here in  particular the proof for the second Lemma, I think my question is related to the necessity part of the proof, but it seems to have confused me more than it helped.
Since $f_1$ is negligible, it is smaller than the inverse of any polynomial, for all sufficiently large $n$. In particular, given any polynomial $q$, it is smaller than $1/p_1q$.