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Thread: Even more factoring!

  1. #1
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    Even more factoring!

    9-4x^2: I don't know where to begin with this one. There are no examples in the book and no odd numbered similar problems so that I could possibly reverse engineer the problem.

    12a^2 +24a: for this one I started with 12(a+1)(a+2). From there I went on to several different variations but came up empty. Wait... is 12a(a+2) the right answer?

    Any and all help is much appreciated. Thanks!
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  2. #2
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    The easiest way to do this problem would be to first factor out the -4
    $\displaystyle -4\left(x^2 - \frac{9}{4}\right)$
    Now notice this is a difference of squares so we can factor it as
    $\displaystyle -4\left(x-\frac{3}{2}\right)\left(x+\frac{3}{2}\right)$
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  3. #3
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    Quote Originally Posted by Ingersoll View Post
    9-4x^2: I don't know where to begin with this one. There are no examples in the book and no odd numbered similar problems so that I could possibly reverse engineer the problem.

    12a^2 +24a: for this one I started with 12(a+1)(a+2). From there I went on to several different variations but came up empty. Wait... is 12a(a+2) the right answer?

    Any and all help is much appreciated. Thanks!
    Assuming you want to write these as a pair of factors...

    $\displaystyle 9-4x^2$ is the "difference of two squares"

    $\displaystyle 3^2-(2x)^2=(3-2x)(3+2x)$

    Notice when you multiply this out you get $\displaystyle (3+2x)(3-2x)=3(3-2x)+2x(3-2x)=3^2-6x+6x+2x(-2x)$




    You correctly corrected yourself on the other.

    Sorry Bacterius...let's call it a dead-heat!
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  4. #4
    Super Member Bacterius's Avatar
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    There is an easier way for the first one ... Just note that $\displaystyle 4x^2 = (2x)^2$ and you already have a difference of squares, without fractions.

    EDIT : beaten to it
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  5. #5
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    Okay. The reason I was having difficulty with it is because it appeared to have been written backwards. As 4x^2 -9, I'm okay. So then what I should do when a difference of squares problem is written this way is to simply rewrite it as 4x^2 -9 and proceed normally?






    You correctly corrected yourself on the other.

    Sorry Bacterius...let's call it a dead-heat![/QUOTE]
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  6. #6
    Super Member Bacterius's Avatar
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    So then what I should do when a difference of squares problem is written this way is to simply rewrite it as 4x^2 -9 and proceed normally?
    Why would you want to do that ? Just notice that $\displaystyle 4x^2$ is a square as well as $\displaystyle 9$ and off you go, right ?

    Sorry Bacterius...let's call it a dead-heat!
    It's ok, I really need we need some sort of mutex system on MHF where people can be warned that someone has posted just before them ... so they can reconsider their post. I might bump the idea soon if no-one can be bothered to notify it.
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  7. #7
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    [QUOTE=Ingersoll;541232]Okay. The reason I was having difficulty with it is because it appeared to have been written backwards. As 4x^2 -9, I'm okay. So then what I should do when a difference of squares problem is written this way is to simply rewrite it as 4x^2 -9 and proceed normally?
    [QUOTE]

    $\displaystyle 4x^2-9=(2x)^2-(3)^2=(2x-3)(2x+3)$

    $\displaystyle 9-4x^2=(3)^2-(2x)^2=(3-2x)(3+2x)=-(2x-3)(3+2x)=-(4x^2-9)$
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  8. #8
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    Quote Originally Posted by Ingersoll View Post
    Okay. The reason I was having difficulty with it is because it appeared to have been written backwards. As 4x^2 -9, I'm okay. So then what I should do when a difference of squares problem is written this way is to simply rewrite it as 4x^2 -9 and proceed normally?
    As others have pointed out $\displaystyle x^2- y^2$ and $\displaystyle y^2- x^2$ are both the "a difference of squares"- but not the same thing: $\displaystyle 4x^2- 9$ and $\displaystyle 9- 4x^2$ are different expressions and have different factorings.

    You could have written $\displaystyle 9- 4x^2= -(4x^2- 9)= -(2x-3)(2x+3)$ but $\displaystyle 9- 4x^2= (3- 2x)(3+ 2x)$ is simpler.






    You correctly corrected yourself on the other.

    Sorry Bacterius...let's call it a dead-heat!
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