Big-O notation finding c and n0

Question

I\'ve just been introduced to Big-O notation and I\'ve been given some questions. However I\'m confused as to how to determine the value of n0. I have to show that

Answer 1

3n^3 + 20n^2 + 5 <= cn^3

5 + 20n^2 <= n^3(c - 3)

5/n^3 + 20/n <= c - 3

For n0 = 20, c >= 5, since 5/n^3 + 20/n < 2