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Math Help - Factorising a quadratic trinomial

  1. #1
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    Exclamation Factorising a quadratic trinomial

    Factorise the following:

    6x^2-11x-10
    Last edited by mr fantastic; October 17th 2009 at 09:43 PM. Reason: Changed post title
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by Tessarina View Post
    Factorise the following:

    6x^2-11x-10
    6x^2-11x-10

    =6x^2-15x+4x-10

    =3x(2x-5)+2(2x-5)

    =(2x-5)(3x+2)
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  3. #3
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    Hello Tessarina
    Quote Originally Posted by Tessarina View Post
    Factorise the following:

    6x^2-11x-10
    (3x+2)(2x-5). Was there a particular problem with this one?

    Grandad
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  4. #4
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    Quote Originally Posted by Tessarina View Post
    Factorise the following:
    6x^2-11x-10
    Hi Tessarina,
    this might assist:

    The factors of 6 (call them a & c)
    1 x 6 = 6
    2 x 3 = 6

    The factors of 10 (call them b & d)
    1 x 10 = 10
    2 x 5 = 10
    Since -10 is negative you know that one of the signs will be.

    You are looking for this form:
    (ax - b)(cx + d) or (ax - d)(cx + b)

    We already know the factors (coefficients) that will give: 6x^2 & -10

    We are seeking the middle part
    such that
    ax*d - cx*b = -11x
    or
    ax*b - cx*d = -11x

    We are trying to find -11x in the following:
    --------------------------------------
    plugging in the factors (1,6 & 1,10)
    (1x - 1)(6x + 10)
    1x*10 - 6x*1 = 4x (does not equal -11x)
    or
    (1x - 10)(6x + 1)
    1x*1 - 6x*10 = -59 (does not equal -11x)


    plugging in the factors (1,6 & 2,5)
    (1x - 2)(6x + 5)
    1x*5 - 6x*2 = -1x (does not equal -11x)
    or
    (1x - 5)(6x + 2)
    1x*2 - 6x*5 = -28x (does not equal -11x)


    plugging in the factors (2,3 & 1,10)
    (2x - 1)(3x + 10)
    2x*10 - 3x*1 = 17x (does not equal -11x)
    or
    (2x - 10)(3x + 1)
    2x*1 - 3x*10 = -28 (does not equal -11x)


    plugging in the factors (2,3 & 2,5)
    (2x - 2)(3x + 5)
    2x*5 - 3x*2 = 4x (does not equal -11x)
    or
    (2x - 5)(3x + 2)
    2x*2 - 3x*5 = -11x (what is needed ! )


    The result wanted:
    (2x - 5)(3x + 2) = 6x^2 -11x - 10
    ::
    After you do this a few times alexmahone's method will be easy to use and generate the result;
    after a few more times you will be able to do it immediately the way Grandad can.


    The asterisk (*) used above denotes multiplication.
    .
    Last edited by aidan; October 18th 2009 at 01:31 PM. Reason: typo in greeting
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  5. #5
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    Quote Originally Posted by Tessarina View Post
    Factorise the following:

    6x^2-11x-10
    Of related interest: http://www.mathhelpforum.com/math-he...tml#post385857
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