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Homework Help: Two questions involving factoring

  1. Feb 22, 2005 #1
    Hello all. I have two questions involving factoring and I seem to be stuck.

    1) [tex] 5x^\frac {1}{2} - 15x^\frac{3}{2} [/tex]

    I tried it and got: [tex] 5x^\frac {1}{2} (1-3x) [/tex]
    I'm not too sure if you could go any further than this or if there's another way to approach this. The answer seems too simple and knowing my teacher, there's probably a more complicated one. Any thoughts?

    2) [tex] 3(x-6)^2 + 2(x-6)^4 + \frac {3}{x-6} [/tex]

    so far I got: [tex] 3(x-6)^3 + 2(x-6)^5 + 3 [/tex] and taking out a common factor of [tex] (x-6)^3 [/tex] I got: [tex] (x-6)^3 (3+2(x-6)^2) + 3 [/tex]
    I don't think this can be the simplest form so any suggestions or ideas? Thanks for the help.
  2. jcsd
  3. Feb 23, 2005 #2


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    #1) CORRECT

    #2) You forgot to divide thru by (x - 6) after multiplying by (x - 6) in your first step, so your final answer should be:

    [tex] \frac {(x-6)^3 (3+2(x-6)^2) + 3} {x - 6} [/tex]

  4. Feb 23, 2005 #3
    I have a question. Would it be correct then to simplify it even further by dividing the top [tex] (x-6)^3[/tex] with the bottom [tex] (x-6) [/tex] to get an answer of [tex] (x-6)^2 (3+2(x-6)^2)+3 [/tex] or no?
  5. Feb 23, 2005 #4
    It would not be correct to do that because of the +3 on the end.
  6. Feb 23, 2005 #5
    I should learn to look at the question more carefully. Thanks man.
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