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Algebraic Identities

If (x-1), (x+...

Question

If (x-1), (x+1) and (x-2) are factors of x^4+(p-3)x^3-(3p-5)x^2+(2p-9)x+6, then the value of p is: A.1 B.2 C.3 D.4

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Solution

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(x - 1), (x + 1)

(x - 2)

x^{4} + (p - 3) x^{3} - (3 p - 5) x^{2} + (2 p - 9) x + 6

p

(x - 1)

(x - 2)

x^{4} - (p - 3) x^{3} - (3 p - 5) x^{2} + (2 p - 9) x + 6

p

(x + 1)

x^{4} + (p - 3) x^{3} - (3 p - 5) x^{2} + (2 p - 9) x + 6

p

p

x + 1

x^{4} + (p - 3) x^{3} - (3 p - 5) x^{2} + (2 p - 9) x + 6

p

P (x) = (\frac{6}{x}) p^{x} q^{6 - x}, x = 0, 1, 2, . . ., 6

2 P (2) = 3 P (3)

p =

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