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Factor Theorem

If x+1 is a f...

Question

If $(x + 1)$ is a factor of $x^{4} - (p - 3) x^{3} - (3 p - 5) x^{2} + (2 p - 7) x + 6$ , then $p =$

None of these

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$4$

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$2$

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$1$

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Solution

The correct option is B
$4$

If $(x + 1)$ is a factor of

$x^{4} - (p - 3) x^{3} - (3 p - 5) x^{2} + (2 p - 7) x + 6,$
then by putting $x = - 1,$ we get

$1 + (p - 3) - (3 p - 5) - (2 p - 7) + 6 = 0$

$\Rightarrow - 4 p = - 16 \Rightarrow p = 4$

Suggest Corrections

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