# Thread: how to factor with negative coefficient

1. ## 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.

2. Originally Posted by anthonye
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.
$\displaystyle -6x^2 + 15x + 36 = -3(2x^2 - 5x - 12) = -3(2x + 3)(x - 4)$

3. 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?