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Math Help - 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.
    -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 3 as the GCF, then you are left with

    -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 -1.

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

     = -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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