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Math Help - factoring a trinomial

  1. #1
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    Thumbs up factoring a trinomial

    Hi,

    i was wondering if any could tell me the quickest method of factoring this trinomial,

    91+24q+-27q^2

    thanks
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by amcta View Post
    Hi,

    i was wondering if any could tell me the quickest method of factoring this trinomial,

    91+24q+-27q^2

    thanks
    This requires some thinking outside the box:

    First pull out -1:

    -(27q^2-24q-91)

    What we want to do now is apply the grouping technique:

    However, we have to manipulate it in such a way so we can use it.

    Note that -13*7=-91 and -24=39-63.

    Now, let us rewrite the trinomial:

    -({\color{red}27q^2+39q}{\color{blue}-63q-91})

    From the red group, factor out a 3q and from the blue group, factor out a -7.

    Thus we now have:

    -(3q{\color{blue}(9q+13)}-7{\color{blue}(9q+13)})

    Note that both terms have the same factor. Factoring out the blue term, we get:

    \color{red}\boxed{-(3q-7)(9q+13)}

    Hope this makes sense!
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