How to solve complexity problems

Question

I have a problem in algorithm subject.. I have to decide whether 127n^2+n^3−4745n^2 is Ω(n^2) or not. How can I do this? Thanks very much!

Answer 1

$127n^2+n^3−4745n^2$ is equal to $n^3−4618n^2$

There are constants $n_0$ and $c$ such that $n^3−4618n^2 \geq \frac{1}{c}n^2$ for all $n \geq n_0$, so $127n^2+n^3−4745n^2$ is $Ω(n^2)$.