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Math Help - Factorising Cubics

  1. #1
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    Factorising Cubics

    I have asked way too many questions, and Im really sorry if I have bothered you lot too much, but thanks so much for the help I do apprieceate every single comment, and it is a great help to my studies.

    Just a question regarding cubics, I need to factorise
    x^3-kx^2+2kx-k-1, I already know x-1 is a factor. If I want to factorise this via the "long division method" how do you go about in doing that? I'm just confused with all these pronumerals, thanks for the help.
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    Let's call this function \displaystyle P(x) = x^3 - kx^2 + 2kx - k - 1 = 0.

    You can start by evaluating \displaystyle k. Since you know \displaystyle x - 1 is a factor, that means \displaystyle P(1) = 0.
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    What do you necesarily mean by evaluating k?
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    Finding out what value k equals...
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    Oh, I am such an idiot . Its the case of rewriting the equation and solving for k correct?
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    Yes, once you have substituted x = 1 and noted that this is a value that makes the entire polynomial = 0.
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    Yeah, I have subbed x=1 one in, and ended up with 0. Now that I know x-1 is a factor do I go ahead with the long division?
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    Oops, I didn't realise that substituting x = 1 just gives 0 = 0. You can't evaluate k this way.

    When you are doing the long division, you need to treat -k-1 as a single term, and remember that since x-1 is a factor, the remainder will be 0.
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  9. #9
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    \left[ \right] you should try the " "long division method" " on this expression and post you work so we can help.
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