Confused by the GCF of a trinomial.

K, so I was taught that if a problem looked like this -12x^3y^5 - 9x^2y^2 + 12xy^3 that first you take the GCF out. So I took 3xy^2 out. I got the answer wrong though because they were telling me to take out a negative as well. But why? I mean,they dont have a negative in common because one is positive. I put for the answer 3xy^2(-4x^2y^3 - 3x + 4y),got it wrong and I'm just wondering why.
Thanks! :)

you're not wrong, but there's a custom to make the 1st term of the trinomial have a positive coefficient so that it's easier to factor into 2 binomials (if that's possible). if that custom was not discussed openly, you should fight for your rights.

-12x^3y^5 - 9x^2y^2 + 12xy^3

- 3xy^2( 4x^2y^3 + 3x - 4y )

Maybe because there are two negatives and has only one positive.
The negative is prioritize because it has two monomials,
while the other positive has only one monomial.
Therefore the sign is negative.

Have you thought of the addition of unlike signs???
When you add the two unlike signs, copy the sign of the higher value.
Got my point?
Two negatives are greater than one positive,
so even the signs are included when finding the GCF, hahaha.... funny, but true! = )
Example, -2 + 1 = - 1 .... Got my point?
So the GCF should be also negative

Wish my answer helped you ! Good Luck ! = )

you got it right but you have to but negtive sign in front
-3 x y^2 (3 x-4 y+4 x^2 y^3), because you have if you multipay the -3xy^2 by (3 x-4 y+4 x^2 y^3)
will give (3 x-4 y+4 x^2 y^3) so remember when when take gfc make sure if you multiplay it you will get the same excat output

i hope that it help
and sorry for my english if is not clear