<s>[INST] calculus - solving limit with complex polynomial I'm try to solve $\lim \limits_{x \to -2} \dfrac{x^3 - x^2 - x + 10}{x^2 + 3x + 2}$.
I have simplified it down to $\lim \limits_{x \to -2} \dfrac{(x + 2)(x^2 - 3x + 5)}{(x + 2)(x + 1)}$.
The solution is $-15$.
However, I can't wrap my mind around it. $(x^2 - 3x + 5)$ has only complex roots because $\Delta < 0$, so how am I supposed to reach the real number $-15$ as the solution?
 [/INST] The roots of $x^2-3x+5$ are irrelevant here. You can simplify and then simply evaluate at $x=-2$ :
\begin{align}
\lim \limits_{x \to -2} \frac{(x + 2)(x^2 - 3x + 5)}{(x + 2)(x + 1)} &= \lim \limits_{x \to -2} \frac{x^2 - 3x + 5}{x + 1} \\
&= \frac{(-2)^2-3(-2)+5}{(-2)+1} \\
&= -15
\end{align}
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