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Math Help - Factoring Question

  1. #1
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    Factoring Question

    I am trying to figure out how to factor out any common factors out of this polynomial: 4(x2+4)3/2(3x+5)1/3 + (3x+5)4/3(x2+4)1/23x
    What I thought to do was to look for each base raised to the smallest exponent present in each term. Looking at the polynomial it looks like (3x+5)1/3, and (x2+4)1/2 are the bases raised to the lowest exponent because 3/2 > 1/2, and 4/3>1/3 therefore I tried to factor these out. When I try to do this I end up with 4(x2+4)2/2+(3x+5)3/33x[(3x+5)(x2+4)], and when I multiply the two binomials in the brackets I get 3x3+5x2+12x+20.
    The answer in the text is (3x+5)1/3(x2+4)1/2(13x2+15x+16). I don't see how they arrived at this, and I also don't see how you could arrive at the original polynomial through multiplication of the terms in the answer. If someone could tell me what I am doing wrong, and explain how to arrive at the correct answer I would really appreciate it. Thanks a lot, I love this site.
    Last edited by KhanDisciple; November 26th 2012 at 01:38 PM.
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  2. #2
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    Re: Factoring Question

    There is a mistake in your simplification

    It is (x^2+4)^(1/2) (3x+5)^(1/3) { 4(x^2+4) + 3x(3x+5)} This will give you the text answer.
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  3. #3
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    Re: Factoring Question

    Thanks for the reply, however I still don't understand how the bases raised to the 3/2, and 4/3 are less than the bases raised to the 1/3 and 1/2 (or then why if the bases (x2+4)^3/2, and (3x+5)^4/3 aren't less than the others why are they the terms that are factored out).
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  4. #4
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    Re: Factoring Question

    Quote Originally Posted by KhanDisciple View Post
    Thanks for the reply, however I still don't understand how the bases raised to the 3/2, and 4/3 are less than the bases raised to the 1/3 and 1/2 (or then why if the bases (x2+4)^3/2, and (3x+5)^4/3 aren't less than the others why are they the terms that are factored out).
    they're not ...

    when you factor (x^2+4)^{1/2} out from (x^2+4)^{3/2} you get (x^2+4)^{1/2}\left[(x^2+4)^1]

    check it by distributing the common factor
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  5. #5
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    Re: Factoring Question

    Thank you for clarifying skeeter, I see what I was doing wrong now.
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