Given $tan (A) = \frac{1}{2}$ and $tan (B) = \frac{1}{3}$ , compute $tan (A + B)$ .

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Find the value of $k$ such that the polynomial $P (x) = 2 x^{3} - 3 x^{2} + k x - 6$ is divisible by $(x - 2)$ .
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