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If $x^{2} + p x + q$ is exactly divisible by $x + 2$ and leaves remainder 5 when divided by $x - 3$ then $p - q$ is

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$0$

$- 4$

$4$

$1$

answer is C.

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Detailed Solution

$p (x) = x^{2} + p x + q$

$p (- 2) = 0$

$4 - 2 p + q = 0$

$- 2 p + q = - 4$

$p (3) = 5$

$9 + 3 p + q = 5$

$3 p + q = - 4$

$p = 0$ then $q = - 4$

$p - q = 0 + 4 = 4$

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