# When do you factor out a negative?

When factoring trinomials, when do you actually factor out a negative, is it if 2/3 of the numbers are negative, or...

Just kinda confused, exams are in a couple days so responses are really appreciated. Thanks!

### 8 Answers

- ElaineLv 76 months agoBest Answer
If the term with an exponent 2 or more is negative factor out -1 as the expression becomes much easier to factor.

- 6 months ago
Well, personally I like to when the leading coefficient is positive. You can get the same answer if you don't do that though. It's preference

- L. E. GantLv 76 months ago
When it simplifies the process...

Usually, it is easier to see the factoring of, say, (x^2 + x - 6) than it is to see the factoring of 6 -x -x^2 but the roots are the same

look at the quadratic formula for both:

x^2 + x - 6 ==> x = (-1 +/- sqrt(1 -4*1*(-6)))/2 = (-1 +/- 5)/2 = -3 or 2

so (x+3)(x-2)

-x^2 -x + 6 ==> x = (1 +/- sqrt( 1 -4*(-1)*6))/(-2) = (1 +/- 5)/(-2) = -3 or 2

so (2-x)(3+x) ==> -(x+3)(x-2)

Which is easier to work out?

Of course, the graphs of the two are different -- one convex upwards, the other convex downwards, but the roots or factors are the same.

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- llafferLv 76 months ago
My rule of thumb is if the leading coefficient is negative, I factor it out, then attempt to factor what's left.

- Anonymous6 months ago
negative and positive.

- 6 months ago
When I'm factoring, I like for the leading coefficient of the highest powered variable to be positive. For instance:

x^2 - 5x - 6

-x^2 + 5x + 6

Both have the same roots, but I like the first form better than the 2nd. My goal is that when it's factored, I get a list of: (x - a) * (x - b) * (x - c) * ...., rather than (-x + a) * (x - b) * (x - c) * ....

-(x^2 - 5x - 6)

-(x - 6) * (x + 1)

-(x - 6) * (x + 1) is the same as:

(6 - x) * (x + 1)

or

(x - 6) * (-x - 1)

But -(x - 6) * (x + 1) looks better to me.

so if the unit of highest powered variable, for example -x^2 was negative, I would factor it out? The other numbers are irrelevant in that case?