Finding the zeros/poles of a function

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My textbook has the following function and states that this function has poles at $0, −1, −2, ∞$:

$$ G(s)=\dfrac{e^{-2s}}{10s(s+1)(s+2)} $$

I understand where the $0,-1$ and $-2$ are coming from but where is the infinity coming from also shouldn't there be zeros at $∞$ as well?

Can someone please help explain this?

Please feel free to edit the tags, thank you.

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Considering only the zeros of

$$ G(s) = e^{-2s} $$

making $s = x + i y$ and substituting we have that $G(s)=0$ can be written as

$$ \cases{ e^{-2x}\cos(2y) = 0\\ e^{-2x}\sin(2y) = 0 } $$

so we have an improper zero as $x\to\infty$