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Math Help - exam preparation

  1. #1
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    exam preparation

    Hi there,

    can anyone help me with this question from my practice exam?

    r(x) = (x^3 + x^2 + 2x) / x ( x - 1)

    i need to write r(x) as p(x) + t(x)/q(x), for polynomials p,t and q with deg(t) < deg(q)

    Thanks
    Last edited by jameyt; November 26th 2009 at 12:27 AM.
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  2. #2
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    Not sure if this is how you should do it, but it seems to make sense to me.

    r(x) = (x^2 + x + 2)/(x-1)
    r(x) = [(x^2 + x -2) +4]/(x-1)
    r(x) = (x+2) + 4/(x-1)
    Last edited by Arturo_026; November 26th 2009 at 12:38 AM.
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  3. #3
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    i have the answer here:

    just not sure how to get it........:


    x + 2 + 4x / (x^2 - x)
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  4. #4
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    Quote Originally Posted by jameyt View Post
    i have the answer here:

    just not sure how to get it........:


    x + 2 + 4x
    x^2 - x
    Is this what you mean: (x+2) + (4x)/(x^2 -x)
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  5. #5
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    yes sorry
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  6. #6
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    Ok, sorry, I made an error in my first answer.
    So here it is again, It's basically the same process but this time I won't cross out the x at the beginning:

    r(x) = [x(x^2 + x + 2)]/(x^2-x)
    r(x) = [x[(x^2 + x -2) +2 +2]]/(x^2-x) .... notice I added and subtracted 2 to get a factorable form

    r(x) = [x(x+2)(x-1)]/[x(x-1)] + 4x/(x^2-x) ... simplify

    r(x) = (x+2) + 4x/(x^2-x)

    Write it out so you can see the process better.
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