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Homework Help: Factoring with factorial exponents.

  1. Sep 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Factor x + 5+ 6x^-1
    Factor x^(3/2) + 2x^(1/2) - 8x^(-1/2)

    2. Relevant equations

    None given.

    3. The attempt at a solution

    I have tried factoring normally, it's just not working out though (for either part of the question.) I've never had to deal with this in a math class before, but my teacher is doing this as part of a review before calculus. If someone could show me what I need to do, I would really appreciate it and would be able to apply it to the rest of the worksheet.
  2. jcsd
  3. Sep 6, 2012 #2
    When you are normally factoring an expression, say [itex]x^3+2x^2+x[/itex], you factor the largest factor of each term out of the expression, in this case, the [itex]x[/itex], or [itex]x^1[/itex] (same thing): [itex]x(x^2+2x+1)[/itex]. Can apply that same logic to the case when the exponent is negative, fractional, or both? Hint: What is the smallest degree of [itex]x[/itex] in the second expression you gave?
    Last edited: Sep 6, 2012
  4. Sep 6, 2012 #3


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    The very first thing you could do is factor out [itex]x^{-1}[/itex] giving
    [itex]x^{-1}(x^2+ 5x+ 6)[/itex]. Can you continue that?

    If you factor out [itex]x^{-1/2}[/itex] you get [itex]x^{-1/2}(x^2+ 2x- 8)[/itex]

  5. Sep 6, 2012 #4


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    Those are fractional exponents, not factorial exponents.
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