Big-Theta:What happens if $\displaystyle{a_d<0}$?

Question

If $\displaystyle{f(n)=an^2+bn+c}$ with $\displaystyle{a>0}$ then $\displaystyle{f(n)=\Theta{(n^2)}}$.

Generally, if $\displaystyle{f(n)=\sum_{i=0}^{d}a_in^i}$ with $\displaystyle{a_d>0}$ then $\displaystyle{f(n)=\Theta{(n^d)}}$.

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But what happens if $\displaystyle{a_d<0}$ ??

Answer 1

It's also $f(n)=\Theta(n^d)$, multiply inequalities in definion of $\Theta(n^d)$ by $-1$.