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

##### 2 Answers

In

In

#### Explanation:

In some cases, you can "see" how to factor such a term with some experience.

Here, for example, you could do the following transformation:

As

=============================

Note: in

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Now, how do you do the factorization if you don't "see" my steps from above?

First, find **one** root.

Generally, you can start with plugging

Here, it's obvious that

Afterwards, perform a polynomial division of

*I know that in some countries, the notation for long division is different. I will write it in the notation that I'm familiar with and I hope that it will be easy for you to re-write it in your notation if necessary.*

This means that you can factor your polynomial as follows:

Finding a factorization for

In

In

An alternative method included for fun...

#### Explanation:

Notice that

So the zeros of this cubic are the

In the Complex plane the

graph{(x^2+y^2-1)((x+1)^2+y^2-0.004)(x^2+(y-1)^2-0.004)(x^2+(y+1)^2-0.004)((x-1)^2+y^2-0.004) = 0 [-2.812, 2.814, -1.406, 1.406]}

That is

So

and