I realize that this is not a typical programing question but its still related. If anyone could help me out I would really appreciate it because I have a midterm coming up and this is the part that I don't understand. This is not a homework problem so don't worry about me trying to get out of my work. I just need someone to explain how to do this is normal plain english instead of whatever my professor is using.
Let $p(n) = \sum_{i=0}^d a_i n^i$ where $a_i,d > 0$ be a polynomial in $n$ of degree $d$. Use the definitions of the asymptotic notations to prove the following properties:
a) If $k \geq d$, then $p(n) = O(n^k)$.
There are also 4 more correspoding to the Omega, theta small o and small omega properties but if I could get an idea on how to start I can figure the other ones out on my own. Thanks so Much!