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If $x + 1$ is a factor of $x^{4} + (p - 3) x^{3} - (3 p - 5) x^{2} + (2 p - 9) x + 6$ , then the value of p is

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-4

answer is C.

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Detailed Solution

Put x = -1 in
$x^{4} + (p - 3) x^{3} - (3 p - 5) x^{2} + (2 p - 9) x + 6$
$1 - p + 3 - 3 p + 5 - 2 p + 9 + 6 = 0 \Rightarrow p = 4$

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