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Math Help - More Factoring

  1. #1
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    More Factoring

    2y^2 -7y +3

    Up until now I've been pretty adept at coming up with the necessary numbers for the middle monomial but for some reason this one and similiar ones like 3y^2 +5y -2 are killing me. I'm pretty sure this is an easy fix but what method should I use?

    Thank you in advance.
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by Ingersoll View Post
    2y^2 -7y +3

    Up until now I've been pretty adept at coming up with the necessary numbers for the middle monomial but for some reason this one and similiar ones like 3y^2 +5y -2 are killing me. I'm pretty sure this is an easy fix but what method should I use?

    Thank you in advance.
    Assuming we can factor just using integers, there are four possibilities to begin with, just based on the coefficient 2 in 2y^2.

    (2y + u) (y + v)
    (2y + u) (y - v)
    (2y - u) (y + v)
    (2y - u) (y - v)

    Seeing the + in front of the three, we can narrow down to

    (2y + u) (y + v)
    (2y - u) (y - v)

    Seeing the - in front of the 7y, we can narrow down to

    (2y - u) (y - v)

    possible (u,v) are (1,3), (3,1), giving

    (2y - 1) (y - 3)
    (2y - 3) (y - 1)

    A little examination reveals

    (2y - 1) (y - 3)

    In practice you can do most of the steps in your head, I would just write

    Code:
    (2y -    )(y -    )
    and then fill in the blanks.
    Last edited by undefined; July 25th 2010 at 01:04 AM. Reason: clarity, typos
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  3. #3
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    A simple method !

    [PHP][/PHP]There is a quite simple method for this equation !  \ \ ax^2+bx+c \ \

    You have to find two numbers so that there multiplication become  \ \ a\cdot c \ \ and there sum is like  \ \ b \ \ for example:

     \ 2y^2-7y+3 \ \ \ we \ can \ see \ that  (-1,-6) is \ the \ suitable \ numbers \ so \ that \ \ 2y^2-6y-y+3 \ \ become \ \ 2y(y-3)+(y-3) = (y-3)(2y+1) \ \

    and 3y^2 +5y -2 \ (-1,6) \ become \ 3y^2+6y-y-2 \ and \  become \ 3y(y+2)-(y+2) = (y+2)(3y-1) \ \ \
    Last edited by yehoram; July 24th 2010 at 09:23 PM.
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