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  1. #1
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    hi i've got a question i'd like some help with:

    given that P(x), where P(x) = x^3 + 3x^2 + kx + 4 and k is a constant, is such that the remainder on dividing P(x) by (x - 1) is three times the remainder on dividing P(x) by (x + 1), find the value of k

    could someone show me the steps to do this please? thankyou
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  2. #2
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    Quote Originally Posted by mark View Post
    hi i've got a question i'd like some help with:

    given that P(x), where P(x) = x^3 + 3x^2 + kx + 4 and k is a constant, is such that the remainder on dividing P(x) by (x - 1) is three times the remainder on dividing P(x) by (x + 1), find the value of k

    could someone show me the steps to do this please? thankyou
    When p(x) is divided by (x - a) the remainder is p(a) (this is something you should already know).

    Solve the equation p(1) = 3 p(-1) for k.
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  3. #3
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    well i first did P(1) and came up with k = -7 but i'm not sure what to do after that? i tried putting 3p(-1) and seeing what that came up with but didn't seem to make much sense, can someone show me how its done in steps please because i'm lost
    Last edited by mark; September 19th 2009 at 02:07 AM.
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  4. #4
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    Quote Originally Posted by mark View Post
    well i first did P(1) and came up with k = -7 but i'm not sure what to do after that? i tried putting 3p(-1) and seeing what that came up with but didn't seem to make much sense, can someone show me how its done in steps please because i'm lost
    p(1) = 8 + k.

    p(-1) = 6 - k.

    Substitute these expressions into p(1) = 3 p(-1). Solve for k.
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  5. #5
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    ah, 10 = 4k, so its 2.5, thanks
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