# How do you factor #x^3-2x^2+4x-8#?

##### 1 Answer

#### Answer:

#### Explanation:

Because this is a third degree polynomial, we have 3 solutions. There's a cubic equation (just like the quadratic equation) but it's really hard so let's try and be smart about this!

We can use the rational root theorem, which states that any solution will be a factor of the

We therefore should try out the following numbers to be roots:

By rational roots theorem, all rational roots are going to be in that list, which makes our job a lot easier.

At this point, we sort of have to plug and chug.

Let's try them in order:

**x = -1**

**x = 1**

**x = -2**

**x = 2**

So

i.e. the polynomial factors to

Depending on what you want, this may be the last step. However, if you understand complex numbers, you may want to go one more step. The second half of the polynomial has roots at