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  1. #1
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    Math Question! Not homework!

    Okay guys I have been starting to review my old math warming myself up for college placement tests and I have run into a problem I can not figure out, nor can my buddy who is about the graduate with a CS degree, -_-. The problem is shown below.

    (2x^2-3x-2) / (10+x-3x^2)

    It needs to be reduced to the lowest term. I have used my ti-89 to get the answer which is -2x-1/3x , but I just don't know how to get there; and don't and can't rely on my calc for the answer. Some help would be nice, even pointing out a rule or equation I have obviously forgotten.

  2. #2
    The Site Administrator: Currently at home recovering from a couple of strokes,please contact my assistnt admins for forum issues Tom Stormcrowe's Avatar
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    Hmm, I get (2X+1)/(3X+5)

    Top:
    2X-3X-2= (2X+1)(X-2)

    Bottom10+x-3X= -1(3X-X-10)=(3X+5)(X-2)

    (2X+1)(X-2)/(3X+5)(X-2)

    (X-2) cancels: Property of One

    Result= (2X+1)/(3X+5)
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  3. #3
    Senior Member Keith99's Avatar
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    You factor the top and you factor the bottom.

    General form of each will be (ax+b)*(cx+d) note any of a b c d may be negative.

    D@mn terms escape me right now.

    a*c has to equal what you multiply x^2 by. b*d has to equal the simple number involved.

    so for (2x^2-3x-2)
    a*c = 2 and b*d= 2

    so you have (2x ? 2) * (x ? 1) or (2x ? 1) * (x ? 2)
    somehow the middle term has to be 3 only way that works is (2x ? 1) * (x ? 2) with 4-1 getting 3.

    from there just play with the signs til it fits.

    When factoring always check by multiplying it out. That is easy and will catch a lot of silly mistakes.

    EDIT:
    Of course as soon as I post I remember coeffecient.

    This really is easy stuff, but lots of people for some reason go blank as soon as the x squared term has a coeffecient. This is the kind of stuff where practice helps. Remember if it can be factored the coeffecients have to be integers. Also remember if they give one where they are not integers to start multiply (both sides) to get to integers before trying to factor.

  4. #4
    Jewish Media Conspirator asherlighn's Avatar
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    Quote Originally Posted by Tom Stormcrowe View Post
    Hmm, I get (2X+1)/(3X+5)

    Top:
    2X-3X-2= (2X+1)(X-2)

    Bottom10+x-3X= -1(3X-X-10)=(3X+5)(X-2)

    (2X+1)(X-2)/(3X+5)(X-2)

    (X-2) cancels: Property of One

    Result= (2X+1)/(3X+5)
    You forgot your factored out -1.
    Im getting (2x-1)/(-3x-5)

    If you factor the -1 out of that answer you get something similar to the OP's calculator, just with an additional +5 in the denominator [(-2x+1)/(3x+5)]. Not sure how your calc got that OP.

    Edit: To the OP: The easy way to simplify binomials is using the F.O.I.L. method (First, Outer, Inner, Last). An explanation can be found here or in any algebra text book.
    Quote Originally Posted by dutret
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  5. #5
    The Site Administrator: Currently at home recovering from a couple of strokes,please contact my assistnt admins for forum issues Tom Stormcrowe's Avatar
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    Quote Originally Posted by asherlighn View Post
    You forgot your factored out -1.
    Im getting (2x-1)/(-3x-5)

    If you factor the -1 out of that answer you get something similar to the OP's calculator, just with an additional +5 in the denominator [(-2x+1)/(3x+5)]. Not sure how your calc got that OP.

    Edit: To the OP: The easy way to simplify binomials is using the F.O.I.L. method (First, Outer, Inner, Last). An explanation can be found here or in any algebra text book.
    By gum, I just looked back and I sure did forget I factored out the neg1! Whoops!
    on light duty due to illness; please contact my assistants for forum issues. They are Siu Blue Wind, or CbadRider or the other 3 star folk. I am currently at home recovering from a couple of strokes. I am making good progress, happily.


    . He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you.- Fredrick Nietzsche

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  6. #6
    cab horn
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    Quote Originally Posted by Diggidy View Post
    nor can my buddy who is about the graduate with a CS degree, -_-.
    That's too bad as any decent college/uni should've covered this first semester, first year. If not even in highschool.
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  7. #7
    Jewish Media Conspirator asherlighn's Avatar
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    Quote Originally Posted by operator View Post
    That's too bad as any decent college/uni should've covered this first semester, first year. If not even in highschool.
    They wont get the answer his calc gave him. Im going to guess the OP entered it in incorrectly.
    Quote Originally Posted by dutret
    The fact is that most peoples sense of what rides well is easily overcome by their sense of what looks cool.

  8. #8
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    I guess I just missed typing the +5 at the end. Thanks guys, I was trying it a different way. I could have sworn remembering a rule where is you have a negative in either the top or bottom you can switch them to the other. So like x-2/x-3 = x+3/x+2, but I knew that wasn't right and just had a brain fart. 2 months away from a textbook and things aren't coming back fast. Thanks for the help guys.

  9. #9
    The Site Administrator: Currently at home recovering from a couple of strokes,please contact my assistnt admins for forum issues Tom Stormcrowe's Avatar
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    No worries, I haven't done any factoring all Summer, so I got a tad hazy and forgot the -1 factored out anyway......

    Thanks, I restart Fall Semester Monday and I'll likely have to do some factoring for n groups anyway for Sociology or Anthropology for statistical studies.
    on light duty due to illness; please contact my assistants for forum issues. They are Siu Blue Wind, or CbadRider or the other 3 star folk. I am currently at home recovering from a couple of strokes. I am making good progress, happily.


    . He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you.- Fredrick Nietzsche

    "We can judge the heart of a man by his treatment of animals." - Immanuel Kant

  10. #10
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    I know what you mean, two months ago I wouldn't had even needed to think about this problem; but algebra has not been a huge focus(not at all actually ) over the summer so the factor thing just seemed to leave my brain space.

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