The polynomial $x^{3} - 2 x^{2} + a x + 6$ has $x - 2$ as a factor. Find the value of $a$ .

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Find the remainder when $P (x) = x^{3} + 2 x^{2} - 3 x + 2$ is divided by $x - 5$ .
Find the remainder when $P (x) = x^{3} + 3 x^{2} - 3 x + 2$ is divided by $x + 4$ .
Find the remainder when $P (x) = x^{3} + x^{2} - 3 x + 2$ is divided by $x - 6$ .
Find the remainder when $P (x) = x^{3} + 4 x^{2} - 3 x + 2$ is divided by $x - 3$ .
Find the remainder when $P (x) = x^{3} - 2 x^{2} - 3 x + 2$ is divided by $x - 7$ .
Find the remainder when $P (x) = x^{3} + 5 x^{2} - 3 x + 2$ is divided by $x - 1$ .