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Math Help - Factoring

  1. #1
    Junior Member Freaky-Person's Avatar
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    Factoring

    Well we had this question on our test today, question number 1 at that, and I just want to know how it's done...

    btw, I don't think I did that bad on the test, it's just number 1 was hard. I think.

    27x^3 - 37y^3 - 64


    If someone could show me the solution and its steps that would be superly awsome.

    Edit: oops. the question asked to factor this fully.
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  2. #2
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    Krizalid's Avatar
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    Quote Originally Posted by Freaky-Person View Post
    27x^3 - 37y^3 - 64
    37y^3=64y^3-27y^3

    I think that's enough to kill the problem.
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  3. #3
    Junior Member Freaky-Person's Avatar
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    Quote Originally Posted by Krizalid View Post
    37y^3=64y^3-27y^3

    I think that's enough to kill the problem.
    why are they all y cubed? O.o

    What happened?

    Yeah you killed the problem alright, and a piece of my respect really...
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  4. #4
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    Are you sure that's the problem?

    I think Krizalid did that because he noticed 64-37=27 and then the answer would be  y \in \mathbb{R} because 27y^{3}=27y^{3}
    Last edited by SnipedYou; October 10th 2007 at 04:57 PM.
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  5. #5
    Junior Member Freaky-Person's Avatar
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    Quote Originally Posted by SnipedYou View Post
    Are you sure that's the problem?

    I think Krizalid did that because he noticed 64-37=27 and then the answer would be  y \in \mathbb{R} because 27y^{3}=27y^{3}
    That's the problem EXACTLY. We're supposed to FACTOR it.

    Will someone PLEASE come up with an answer T.T

    27x^3 - 37y^3 - 64
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  6. #6
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    Well you can get the y^{3} onto its own side and then factor
    37y^{3}=(3x-4)(9x^{2}+12x+16) I don't know how to take this any further.
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by SnipedYou View Post
    Well you can get the y^{3} onto its own side and then factor
    37y^{3}=(3x-4)(9x^{2}+12x+16) I don't know how to take this any further.
    you cannot introduce an equal sign if it was not there in the first place. in doing so you are assuming the formula was equal to zero. we were not given such information
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  8. #8
    Junior Member Freaky-Person's Avatar
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    Quote Originally Posted by SnipedYou View Post
    Well you can get the y^{3} onto its own side and then factor
    37y^{3}=(3x-4)(9x^{2}+12x+16) I don't know how to take this any further.
    That's so awsome, because that's as far as I got on the test,

    question is if it can actually go further. (without the equals, I left it at minus)
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  9. #9
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Freaky-Person View Post
    That's so awsome, because that's as far as I got on the test,

    question is if it can actually go further. (without the equals, I left it at minus)
    (remember, the equal sign is not supposed to be there).

    maybe it's because i'm tired, but i can't see a way to "fully" factor this. it seems you will end up with a plus or a minus sign between terms
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  10. #10
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Freaky-Person View Post

    27x^3 - 37y^3 - 64
    I constructed the most general possible factor and could not reproduce it. This cannot be factored over the rationals.

    -Dan
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  11. #11
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by topsquark View Post
    I constructed the most general possible factor and could not reproduce it. This cannot be factored over the rationals.

    -Dan
    ok, so i'm not crazy

    when you get the paper back, make sure you have the correct question, Freaky-Person
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  12. #12
    Junior Member Freaky-Person's Avatar
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    Quote Originally Posted by Jhevon View Post
    ok, so i'm not crazy

    when you get the paper back, make sure you have the correct question, Freaky-Person
    I swear, that's the question EXACTLY!

    I stared at it for like 5 minutes before I realised my teacher is probably evil enough to put something like that on. I stared at the '37' for god knows how long wishing it to be a perfect cube T.T

    Thanks for all the help though guys. I guess I'll wait for the results.
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  13. #13
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Freaky-Person View Post
    I swear, that's the question EXACTLY!

    I stared at it for like 5 minutes before I realised my teacher is probably evil enough to put something like that on. I stared at the '37' for god knows how long wishing it to be a perfect cube T.T

    Thanks for all the help though guys. I guess I'll wait for the results.
    yes, and when the result comes, tell your professor, "topsquark says this can't be factored, and he's smarter than you!"...don't call my name though, i have enough enemies
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  14. #14
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Jhevon View Post
    yes, and when the result comes, tell your professor, "topsquark says this can't be factored, and he's smarter than you!"...don't call my name though, i have enough enemies
    Ummmm... Thanks Jhevon.

    -Dan
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