I am having trouble understanding the Big-Theta definition and providing a proof.
Prove that $4n^3 + 3n^2 +2n - 5$ is $\Theta(n^3)$.
I believe using the definition the set up would be as followed:
Proof: By Big-Theta Definition Let the above expression be denoted as $T(n)$. $T(n)$ is $\Theta(n^3)$ if $c_1*n^3 \leq |T(n)| \leq c_2*n^3$ for some $n >= n_0$.
This part of solving I am having trouble with:
How do I solve each side to prove that T(n) exists both in $O(n^3)$ and $\Omega(n^3)$?