## Factoring a Quadratic Expression: -6x^2 - 12x + 48

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.

### Factoring a Quadratic Expression: -6x^2 - 12x + 48

The problem I'm having is probably simple, but I can't figure out what I'm doing wrong.

I'm attempting to factor the equation -6x^2-12x+48 into the (x-a)(x-b) format. I managed to find that the two factors that would work would be -24 and 12, as multipled together they equal the product of -6 and 48 while when added together equal -12.

So I tried the box method to attempt to figure out the rest of the values
Code: Select all
`      -6x        -24-6x (-6x^2)     (-24x)12   (12x)       (48)`

By that, the solution should be (-6x-24)(-6x+12), but this is obviously not the case. -6x multiplied by -6x equals 36x^2, not -6x^2. Could someone tell me where I'm messing this up?
Aqua Dragon

Posts: 10
Joined: Sat Apr 11, 2009 3:44 pm

### Re: Factoring a Quadratic Equation

Aqua Dragon wrote:...
By that, the solution should be (-6x-24)(-6x+12), but this is obviously not the case. -6x multiplied by -6x equals 36x^2, not -6x^2. Could someone tell me where I'm messing this up?

you have an extra factor of -6 in your answer...you should have

$(-6x-24)(x-2)$

or

$-6(x+4)(x-2)$

Martingale

Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA

Aqua Dragon wrote:I tried the box method to attempt to figure out the rest of the values...

The "box" method works only after you've taken any common factors out front.

So your first step must be what was explained in the previous reply: take the -6 out front. Only then can you apply "box".

stapel_eliz

Posts: 1708
Joined: Mon Dec 08, 2008 4:22 pm

### Re: Factoring a Quadratic Expression: -6x^2 - 12x + 48

Ah, thank you atapel. Once I got that factor out of the way, I found the answer I wanted. Thanks.
Aqua Dragon

Posts: 10
Joined: Sat Apr 11, 2009 3:44 pm