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Math Help - Find the value of k using long division

  1. #1
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    Find the value of k using long division

    Hello guys, I'm really stuck with this question in my assignment. I just wondering if you can give me an idea how to solve K using long division. Here is the function.

    F(x) = x^5 - 3x^4 + 7x^3 + Kx^2 + 9x - 5; d(x) = x^2 - 1 +1

    What I did here is I divided F(x) by D(x). But I dont know what to do with the K.

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by cjru View Post
    Hello guys, I'm really stuck with this question in my assignment. I just wondering if you can give me an idea how to solve K using long division. Here is the function.

    F(x) = x^5 - 3x^4 + 7x^3 + Kx^2 + 9x - 5; d(x) = x^2 - 1 +1

    What I did here is I divided F(x) by D(x). But I dont know what to do with the K.
    confirm your posted expression for the divisor, D(x), please.
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  3. #3
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    Quote Originally Posted by skeeter View Post
    confirm your posted expression for the divisor, D(x), please.

    Sorry my divisor should be d(x) x^2-x+1
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  4. #4
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    Find the value of K using long division

    My divisor should be d(x) = x^2 - x +1
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  5. #5
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    I did the long division, and assuming the quotient has no remainder, i get k = -11.

    Code:
                   x^3 - 2x^2 + 4x + (k+6)
    .............------------------------------------
    x^2-x+1 | x^5 - 3x^4 + 7x^3 + kx^2 + 9x - 5
                   x^5 - x^4   + x^3
    ..............------------------------------------
                         -2x^4  + 6x^3 + kx^2 + 9x - 5
                         -2x^4  + 2x^3 - 2x^2
    ....................--------------------------------
                                    4x^3 + (k+2)x^2 + 9x - 5
                                    4x^3 -  4x^2    + 4x
    ...............................--------------------------
                                              (k+6)x^2 + 5x - 5
    ....................................... (k+6)x^2 - (k+6)x +(k+6)
                                            -------------------------
    last line ...

    k+6 = -5
    k = -11
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  6. #6
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    Solving for K using a long division

    Thank you very much for helping me. I just wanna clarify something. How did you get (k+2)x^2 .


    2x^4 + 6x^3 + kx^2 + 9x - 5
    -2x^4 + 2x^3 - 2x^2
    --------------------------------
    4x^3 + (k+2)x^2 + 9x - 5
    4x^3 - 4x^2 + 4x
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  7. #7
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    kx^2 - (-2x^2) = kx^2 + 2x^2 = (k+2)x^2
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  8. #8
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    Solving for K using a long division

    On the last line

    (k+6)x^2 + 5x-5
    (k+6)x^2 - (k+6)x + (k+6)

    how did you arrived this "k+6 = -5"

    Thanks you for your patience.
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  9. #9
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    5x - [-(k+6)x] = 0

    5x + (k + 6)x = 0

    k+6 = -5
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  10. #10
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    Thank you very much

    wow! Now everything is clear to me. Thank you very much Mr skeeter.

    Godbless and keep up the good work.
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