Big O notation where C is negative

Question

How do you prove the following?

What I have so far:

Answer 1

$$ 0 < \frac{n^3}{10000} - 100 n^2 - 100n + 3 < \frac{n^3}{10000}$$ for $ n > 200*10000$,

We can pick $C = \frac{1}{10000}$