# How do you factor #x^3+x^2-x-1#?

##### 1 Answer

We must first determine what numbers are factors using the rational root theorem and the remainder theorem.

#### Explanation:

The rational root theorem helps us list all possible factors of a particular polynomial of the form

In our case, the factors of *possible* factors are

The remainder theorem helps to see if a given number is a factor without having to effectuate the full division. If

Let's start with the positive

Yes,

Now, we can use either synthetic or long division to start the factoring process. I will use synthetic, because for me it is extremely efficient and quick at getting the job done.

"*_**_**_**_**_*** _**__"

Hence,

So,

Hopefully this helps!