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    Given that (x - 1) and (x + 1) are factors of px^3 + qx^2 - 3x - 7 find the value of P and Q

    Any help very much appreciated
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    (Original post by Tut)
    Given that (x - 1) and (x + 1) are factors of px^3 + qx^2 - 3x - 7 find the value of P and Q

    Any help very much appreciated
    If (x-1) and (x+1) are factors, f(1) and f(-1) are equal to zero.

    f(1) = p + q - 3 - 7 = 0
    f(-1) = -p + q + 3 - 7 = 0

    q + p = 10
    q - p = 4

    Add the two equations.
    2q = 14
    q = 7

    q + p = 10
    => p = 10 - q = 10 - 7 = 3

    q = 7, p = 3
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    (Original post by Tut)
    Given that (x - 1) and (x + 1) are factors of px^3 + qx^2 - 3x - 7 find the value of P and Q

    Any help very much appreciated
    Alternatively:

    (x-1) and (x+1) are factors. Hence (x-1)(x+1) = x^2 - 1 is a factor.

    You then need to divide px^3 + qx^2 - 3x - 7 by x^2 - 1. You know there is no remainder so you can use this fact when subtracting the rows to find values of p and q.
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    Given that (x - 1) and (x + 1) are factors of px^3 + qx^2 - 3x - 7 find the value of P and Q

    F(1) = p + q - 3 - 7 = 0
    F(-1) = -p + q + 3 - 7 = 0

    p + q = 10
    -p + q = 4

    Solving simultaneously

    2q = 14
    q=7

    p + q = 10
    p + (7) = 10
    Therfore, p = 3
 
 
 
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