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Thread: how to factor with negative coefficient

  1. #1
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    how to factor with negative coefficient

    Hi all;
    not quite sure how to factor -6x^2 +15x +36 first removu GCF of 3,now does this give -3(2x^2 + 5x + 12) or -3(2x^2 - 5x -12) it must factor to the second trinomial I'm sure I'm right because the first one would factor out to

    -6x^2 -15x -36 which is not the original so the second one muat be right I just need confirmation that it factors out to the red version.

    Thanks.
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  2. #2
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    Quote Originally Posted by anthonye View Post
    Hi all;
    not quite sure how to factor -6x^2 +15x +36 first removu GCF of 3,now does this give -3(2x^2 + 5x + 12) or -3(2x^2 - 5x -12) it must factor to the second trinomial I'm sure I'm right because the first one would factor out to

    -6x^2 -15x -36 which is not the original so the second one muat be right I just need confirmation that it factors out to the red version.

    Thanks.
    $\displaystyle -6x^2 + 15x + 36 = -3(2x^2 - 5x - 12) = -3(2x + 3)(x - 4)$
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  3. #3
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    Well if you remove $\displaystyle 3$ as the GCF, then you are left with

    $\displaystyle -6x^2 + 15x + 36 = 3(-2x^2 + 5x + 12)$.

    Now if you want to factor the negative, you have to remember that you are taking out a factor of $\displaystyle -1$.

    So that means $\displaystyle 3(-2x^2 + 5x + 12) = -1\cdot 3(2x^2 - 5x - 12)$

    $\displaystyle = -3(2x^2 - 5x - 12)$.


    Do you see how when you take out a negative factor, all of the signs change?
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