Which of the following conjecture is true? Justify

10n = O(n) 10n^2 = O(n) 10n^{55} = O(n^2 )


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

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

How can I solve the other two?

I found this problem on the Internet:
It is true that n^2 + 200n + 300 = O(n^2 ) ? And n^2 -200n -300 = O(n) ?