# Factoring polynomial

1. Nov 8, 2006

### mbrmbrg

I'm going over some math work, and ran across the following:
$$\frac{2x^2-5x-1}{x^3-2x^2-x+2}=\frac{A}{x-1}+\frac{B}{x+1}+\frac{C}{x-2}$$

How do you get $$x^3-2x-x+2=(x-1)(x+1)(x-2)$$?

2. Nov 8, 2006

### Hurkyl

Staff Emeritus
Well, it's easy to verify that it's right.

To find it... well, one way is that there are only four rational numbers that could possibly be roots of your polynomial, so you just try them!

3. Nov 8, 2006

### mbrmbrg

How so? (pardon me if I be asking heap stupid question; I pulled an all-nighter last night and the brain doth rebel against unwarranted abuse)

4. Nov 8, 2006

### Hurkyl

Staff Emeritus
5. Nov 8, 2006

### mbrmbrg

Why do I feel like someone at PhysicsForums sent me to this webpage before...?

Thanks!

6. Nov 10, 2006

### Tedjn

Sometimes, especially for third degree expressions, you can see if you are able to factor by grouping. Namely,

$$x^3 - 2x^2 - x + 2 = (x^3 - 2x^2) + (-x + 2) = x^2(x - 2) - (x - 2) = (x - 2)(x^2 - 1) = (x - 2)(x - 1)(x + 1)$$