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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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4

1

0

- 4

answer is C.

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Detailed Solution

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

$p (- 2) = 0$

$4 - 2 p + q = 0$

$- 2 p + q = - 4$

$p (3) = 5$

$9 + 3 p + q = 5$

$3 p + q = - 4$

Question Image

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

$p - q = 0 + 4 = 4$

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