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Math Help - Division Algorithm.....

  1. #1
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    Question Division Algorithm.....

    If the polynomial f(x) = ax^3 + bx - c is divisible by the polynomial g(x) = x^2 + bx +c, then ab = ?
    Please Help....
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  2. #2
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    If f(x) is divisible by g(x), the you can write

    ax^3 + bx - c = (px + q)(x^2 + bx - c)

    Expand the brackets and compare coefficients of like powers of x. Write p and q in terms of a, b and c. Then find ab.
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  3. #3
    MHF Contributor chisigma's Avatar
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    If the hypothesis id true is...

    a\ x^{3} + b\ x -c = (a\ x + d)\ ( x^{2} + b\ x + c) (1)

    ... and that means that is...

    a\ b + d=0

    c\ d = -c (2)

    ... so that...

    d=-1

    a\ b=1 (3)

    Kind regards

    \chi \sigma
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  4. #4
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    Question

    Quote Originally Posted by chisigma View Post
    If the hypothesis id true is...

    a\ x^{3} + b\ x -c = (a\ x + d)\ ( x^{2} + b\ x + c) (1)

    ... and that means that is...

    a\ b + d=0

    c\ d = -c (2)

    ... so that...

    d=-1

    a\ b=1 (3)

    Kind regards

    \chi \sigma
    @chisigma ....
    i ve got 2 qestions regarding this....
    1)how did u ax + d to be a multiple of ax^3 + bx - c
    2) and did u get ab + d by opening the brackets?
    pls help.....
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  5. #5
    MHF Contributor chisigma's Avatar
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    Now...

    a) if x^{2} + b\ x + c devides a\ x^{3} + b\ x -c , then there is a first order polynomial a\ x + d so that...

    a\ x^{3} + b\ x -c = (a\ x + d)\ (x^{2} + b\ x + c) (1)

    b) if You develop the product (1) You obtain...

    (a\ x + d)\ (x^{2} + b\ x + c) = a\ x^{3} + (a\ b + d)\ x^{2} + (a\ c + b\ d) x + d\ c = a\ x^{3} + b\ x -c (2)

    c) from the (2) You obtain ...

    a\ b + d=0 , d= -1 \rightarrow a\ b = 1 (3)

    Kind regards

    \chi \sigma
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