Factor

D

Dominic

Junior Member
Joined
Jun 16, 2005
Messages
69
Factor: -x^2 -x -6.

My answer is:

(x - 2)(x - 3)

For some reason I think this is incorrect.
 
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.
 
Dominic said:
(-x + 3)(-x +3)
Click to expand...
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.
 
The only numbers I think of is 2 and 3

So the answer i get is (-x + 2) (-x + 3).
 
-x² - x - 6
Click to expand...

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

those are your four choices.
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.
 
...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
 
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)
 
well, perhaps this'll keep TK happy:
[x + (sqrt(-23)-1)/(-2)][x - (sqrt(-23)-1/(-2)] = 0 :)
 
Much better. :lol:
I think that added quite a bit to the student's understanding. :)
 
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