Word Count : 251

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We are given: $$ f(x) = x^3 - x^2 - 8x + 12 $$ and $$ g(x) = \begin{cases} \frac{f(x)}{x+3}, & x \neq -3 \\ \alpha, & x = -3 \end{cases} $$ First, factor $f(x)$ to see if $x+3$ is a factor. Using the factor theorem, test $x=-3$: $$ f(-3) = (-3)^3 - (-3)^2 - 8(-3) + 12 = -27 - 9 __________ __________ _________ __________ _______ _____.
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