# Factor

#### Dominic

##### Junior Member
Factor: -x^2 -x -6.

(x - 2)(x - 3)

For some reason I think this is incorrect.

#### tkhunny

##### Moderator
Staff member
Multiply it back and see!

(x - 2)(x - 3) = x^2 - 5x + 6

You were RIGHT! It wasn't right.

One thing you should ALWAYS do first is remove factors common to all terms.

-x^2 - x - 6 = -(x^2 + x + 6)

See if you can factor that.

(-x + 3)(-x +3)

#### tkhunny

##### Moderator
Staff member
Dominic said:
(-x + 3)(-x +3)
You're just guessing.

(-x + 3)(-x +3) = x^2 - 6*x + 9

Try again.

-x^2 - x - 6 = -(x^2 + x + 6) = -(x + ___)*(x + ___)

See if you can fill in the blanks with FACTORS OF 6. Don't try ANYTHING that you can't multiply to get 6. 3x3 = 9 Don't try 3x3. Then, multiply it out to see if you get the right thing.

#### Dominic

##### Junior Member
The only numbers I think of is 2 and 3

So the answer i get is (-x + 2) (-x + 3).

#### ChaoticLlama

##### Junior Member
-x² - x - 6
Like tkhunny said, first pull out the common term.

-(x² + x + 6)

Then you think to yourself, what are the factors that multiply to make 6?

1 * 6
-1 * -6
2 * 3
-2 * -3

To figure out which one to use, look at the coefficient of the 'x' term.
The coefficient is 1.

now decide which set of those factors above will add up to 1.

#### tkhunny

##### Moderator
Staff member
...and DON'T try to put that negative thing back in. Leave it factored out. It will confuse you less if you factor it out and leave it there.

By the way:

-(x+6) = -x - 6 It is NOT -x+6

#### Denis

##### Senior Member
What's going on here...

I get x = [1 +- sqrt(-23)] / (-2)

What am I missing?

(-1)x^2 - x - 6 = 0
x = [1 +- sqrt(1 - 4(-1)(-6))] / [2(-1)]
x = [1 +- sqrt(-23)] / (-2)

Arthur

Staff member

#### Matt

##### Junior Member
tkhunny said:
Denis said:
What am I missing?
Only the problem statement.
Denis is correct. It is not possible to factor the expression without complex numbers.

#### Denis

##### Senior Member
well, perhaps this'll keep TK happy:
[x + (sqrt(-23)-1)/(-2)][x - (sqrt(-23)-1/(-2)] = 0

#### tkhunny

##### Moderator
Staff member
Much better. :lol:
I think that added quite a bit to the student's understanding.