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The factorial function from $\mathbb{N}$ to $\mathbb{N}$ is a special case of the gamma function from $\mathbb{C}$ to $\mathbb{C}$:
$$n! = \Gamma(n+1) = \int\limits_{0}^{\infty}{x}^{n}{e}^{-x}\,{\rm{d}}x$$
Unfortunately, this function is defined for all complex numbers except negative integers and zero.
If you mean $-(9!)$, which will often be written simply as $-9!$, then the answer would be $b$, because it is simply $(-1)*(9!)$, or -362800. However, if you mean $(-9)!$, then the answer would be $c$, because the gamma function has poles at the negative integers and zero, because $\Gamma(x)$ can be defined as $\frac{\Gamma(x+k)}{\prod_{j=0}^{k-1}x+j}$ for any $k$ where $x+k>0$. Therefore if $x$ is a negative integer, than one of the factors of the denominator will be zero, and so there will be a pole at all negative integers.