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Math Help - hey guys

  1. #1
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    hey guys

    hey guys. New user here obviously. Hoping to bring my math grades up with help from you guys.

    I was trying to ask a question before but I'm not really sure which section this belongs in.



    I need to graph this equation

    Y=x^3-9x^2+27x-27


    I'm assuming I need to factor it first but I can't figure it out.
    Last edited by ForeverConfused; July 19th 2014 at 11:08 AM.
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  2. #2
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    Re: hey guys

    Quote Originally Posted by ForeverConfused View Post

    I need to graph this equation

    Y=x^3-9x^2+27x-27

    I'm assuming I need to factor it first but I can't figure it out.
    $x^3-9x^2+27x-27$

    well we know that $(-3)^3-=-27$ so let's try $x-3$ as a factor

    $\dfrac{x^3-9x^2+27x-27}{x-3}=x^2-6x+9$

    and it's fairly easily recognized that

    $x^2-6x+9=(x-3)^2$

    so

    $x^3-9x^2+27x-27=(x-3)^3$

    So this is basically $x^3$ but shifted over 3 to the right. You should be able to draw a quick sketch of $x^3$.

    Do this but center it at $x=3$
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  3. #3
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    Re: hey guys

    what do you mean by

    " let's try x−3 as a factor"

    sorry it's been about a year since I last did any maths
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  4. #4
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    Re: hey guys

    Quote Originally Posted by ForeverConfused View Post
    what do you mean by

    " let's try x−3 as a factor"

    sorry it's been about a year since I last did any maths
    I mean assume that $x^3-9x^2+27x-27=f(x) (x-3)$

    where we don't know $f(x)$ yet. We can find it by dividing $x^3-9x^2+27x-27$ by $(x-3)$ and seeing if it comes out even.

    If it does (it does) we know that we were right in guessing $(x-3)$ as a factor.

    If you haven't had math in ages why do you have to graph this function?
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  5. #5
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    Re: hey guys

    Well it's summer break and my parents told me to take advanced functions during the break so it will be easier for me when school starts again
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  6. #6
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    Re: hey guys

    this is the way I did it and got the correct answer for this question and the next

    oh and for the future what section should I post my problems in?

    y=x^3 - 9x^2 - 27x - 27
    =(x^3 - 27)+ (9x^2 - 27x)
    =(x^3-27) -9x (x - 3)
    =(x^3 - 3^3) -9x (x - 3)
    =(x-3)(x^2 + 3x + 9) - 9x(x - 3)
    =(x-3)(x^2 + 3x +9 - 9x)
    =(x-3)(x^2 - 6x +9)
    =(x-3)(x-3)(x-3)
    =(x-3)^3
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  7. #7
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    Re: hey guys

    Looks good to me, good job!

    Pre-Calc would be a likely forum.

    -Dan
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