# Factoring Problem

1. Mar 5, 2006

### Hollysmoke

I was working on this one trinomial problem-2(2x^2+3x-14) but I tried doing foil but I'm not sure what I am doing wrong. Could someone help me out? Thanks.

2. Mar 5, 2006

### Hootenanny

Staff Emeritus
Are you solving for x?

3. Mar 5, 2006

### Hollysmoke

nope. Just trying to factor it.

4. Mar 5, 2006

### HallsofIvy

Well, you can't be "solving for x" since there is no equation! Since you titled this "Factoring Problem", guess you want to factor it further. That "2" in front has already been factored out and you can ignore it (until you are ready to write the answer).

The first step, then, is to factor 2x2+ 3x- 14. When you say you tried "FOIL", I was puzzled for a moment- that's really a mnemonic for multiplying, not factoring. But I suspect you really mean is:
The only way to factor 2 (into integer factors) is 2 and 1 so you must have (2x )(x ). There are two ways to factor 14: 1*14 and 2*7 and since you have -14, that gives -1*14, 1*(-14), -2*7, and 2*(-7)
That is- if it is possible to factor 2x2+ 3x- 14 with integer coefficients it must be one of:
(2x- 1)(x+ 14)
(2x+ 1)(x- 14)
(2x- 2)(x+ 7)
(2x+ 2)(x- 7)
(2x+14)(x- 1)
(2x-14)(x+ 1)
(2x- 7)(x+ 2)
(2x+ 7)(x- 2)
(2x+ 1)(x-14)
(2x- 1)(x+ 14)

Go ahead, multiply them and see if any work. You really only need to check the "cross terms"- the "O" and "I" of FOIL. Of course, there is no guarentee that this can be factored with integer coefficients!

Once you've figured out how to factor 2x2+ 3x- 14, don't forget to write that "2" factor.

5. Mar 5, 2006

### Hollysmoke

(2x+ 7)(x- 2)

Ahh thank you!

6. Mar 6, 2006