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Factor, Remainder and Factorisation

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 =

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Solution

The correct option is A
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) – (3p – 5) – (2p – 7) + 6 = 0

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

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