# Factorizationnof polynomilal

1. Jan 27, 2006

### Feynman

Hello ,
how to factorize the folowing polynomial$$X^4+X^3+X^2+X+1$$

2. Jan 27, 2006

### StatusX

Multiply by (x-1).

3. Jan 27, 2006

### Feynman

can you clarify?

4. Jan 27, 2006

### StatusX

What do you mean how? Just multiply the polynomial by (x-1) and see what you get.

5. Jan 27, 2006

### Feynman

So i need how factorize it in details

6. Jan 27, 2006

### StatusX

I'm not going to give you a step by step explanation of how to do this. That wouldn't really be helping you. Just try multiplying by (x-1). Do you not know how to do this? For example, if you had x2-x+1, multiplying by x-1 would give you (x-1)(x2-x+1) = x(x2-x+1)-(x2-x+1) = x3-x2+x-x2+x-1 = x3-2x2+2x-1.

7. Jan 27, 2006

### Feynman

I Arrivided To X^5-1
So How To Factorise It?

8. Jan 27, 2006

### StatusX

Are you familiar with compex numbers? How about the roots of unity? Try plugging in $e^{i \theta}$, and remember that a fifth degree polynomial has five roots. Also don't forget that 1 isn't really a root, since you multiplied by (x-1).

Last edited: Jan 27, 2006