Which of the following conjecture is true? Justify

10n = O(n) $\displaystyle 10n^2 = O(n) $ $\displaystyle 10n^{55} = O(n^2 ) $

1) $\displaystyle 10n \leq cn$ => $\displaystyle n=1$ $\displaystyle c=10$

$\displaystyle f(n) \leq 10g(n)$ for all $\displaystyle n \geq 1$. $\displaystyle f(n) \in O(g(n))$

How can I solve the other two?

I found this problem on the Internet:

It is true that $\displaystyle n^2 + 200n + 300 = O(n^2 )$ ? And $\displaystyle n^2 -200n -300 = O(n)$ ?