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Math Help - Need a tutorial

  1. #1
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    Need a tutorial

    Hi guys and gals,
    I am reading schaums outline of precalculus 2nd ed. and I am having some issues solving a few of the problems.

    Can someone point me to a tutorial that can help me factor equations like this:

    4x^6-37x^3+9

    I understand how to do the more simple ones like x^2-12x+27 but the one above is throwing me for a curve.
    Thanks you very much.
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  2. #2
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    Re: Need a tutorial

    There is no general formula for solving polynomials of degree 5+ (and even the ones for degrees 3 and 4, the formulas are usually to complicated to implement efficiently), so often you look for tricky factorisations. You don't need it in this case.

    Set x^3=y to get a quadratic 4y^2-37y+9. Solve for y, and then solve x^3=y for x.

    For information about actual factorisations of higher degree polynomials, google 'factoring higher degree polynomials'. I took a look at the first few links and they all seem pretty good, so the choice is yours. Also this youtube video looks good for your case:
    Spoiler:
    Last edited by Gusbob; March 17th 2013 at 04:34 PM.
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  3. #3
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    Re: Need a tutorial

    Thank you so much. I am googleing now
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  4. #4
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    Re: Need a tutorial

    http://www.eowyn.org/teaching/AdvAlg...gherDegree.pdf seemed to explain it well. Going to try some sample problems and see how it goes.
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  5. #5
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    Re: Need a tutorial

    Ok, feel free to post here if you have problems with those.
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  6. #6
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    Re: Need a tutorial

    I stumbled apon another problem that I cant see past. I figured out a,b,c no problem but I dont know how to simplify d. can someone point me in the right direction?
    Need a tutorial-help.jpg
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  7. #7
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    Re: Need a tutorial

    You should post each new question in a new thread. Anyway

    \displaystyle \begin{align*} \frac{p\, x^{p-1}}{q \left( x^{\frac{p}{q}} \right) ^{q-1}} &= \frac{p \, x^{p-1}}{ q\, x^{\left( q - 1 \right) \frac{p}{q} } } \\ &= \frac{p \, x^{p-1}}{ q\, x^{p - \frac{1}{q}} } \\ &= \frac{p}{q} \, x^{ p - 1 - \left( p - \frac{1}{q} \right) } \\ &= \frac{p}{q} \, x^{ \frac{1}{q} - 1 } \end{align*}

    I do not agree with the answer given to you.
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  8. #8
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    Re: Need a tutorial

    I wish I could wrap my head around that... guess I just got to go study more. Thanks for the help.
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