How do you factor #x^3+x^2-x-1#?
We must first determine what numbers are factors using the rational root theorem and the remainder theorem.
The rational root theorem helps us list all possible factors of a particular polynomial of the form
In our case, the factors of
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
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.
Hopefully this helps!