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Math Help - Factoring hard trinomial confusion

  1. #1
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    Factoring hard trinomial confusion

    I have this equation that I need to factor


    The answer to this I am given is


    However no matter how hard I try I cannot seem to get to this solution
    I have tried...

    Step 1
    Multiplying the first term by the last term to get 24

    Step 2
    Finding out what factor of 24 adds to get -10. The answer I get for this is -6 and -4

    Step 3
    With this information, I make a new equation


    Step 4
    I try to do grouping at this point however the answer I get is completely different from


    To be specific, I tried to group with since they share a common factor and did the same logic with grouping with

    However this ultimately leads me with an answer that isn't what I'm given.
    Is there something I am overlooking here? If so, please explain. Much obliged
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  2. #2
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    Re: Factoring hard trinomial confusion

    $\large ax^2 + bx +c=a(x-r1)(x-r2)$

    where

    $r1,r2=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

    in this case

    $r1=\dfrac 3 4, ~r2=\dfrac 1 2, ~a=8$

    $8\left(x-\dfrac 3 4\right)\left(x - \dfrac 1 2\right)=$

    $8\left(x^2-\dfrac{5x}{4}+\dfrac 3 8\right)=$

    $8x^2-10x+3$

    and of course you can distribute the factor of 8 between the 2 factors to get rid of fractions as

    $8\left(x-\dfrac 3 4\right)\left(x - \dfrac 1 2\right)=$

    $4\left(x-\dfrac 3 4\right) \cdot 2\left(x - \dfrac 1 2\right) = $

    $(4x-3)(2x-1)$

    This isn't generally the fastest way to factor a polynomial but it will always work when all else fails.
    Last edited by romsek; March 31st 2014 at 12:23 AM.
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  3. #3
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    Re: Factoring hard trinomial confusion

    Hi,

    you stopped one step before the finish:

    Quote Originally Posted by DanSmith View Post
    I have this equation that I need to factor



    Step 3
    With this information, I make a new equation


    ...
    8x^2-4x-6x+3 = 4x(2x-1) - 3(2x-1) = (2x-1)(4x-3)

    ... but of course it would be better if you learn to master the method romsek showed you.
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