How Do You Factorize X^4+X^3+X^2+X+1?

[Feynman]

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

 

[StatusX]

Multiply by (x-1).

 

[Feynman]

Multiply by (x-1).

How please?
can you clarify?

 

[StatusX]

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

 

[Feynman]

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

So i need how factorize it in details

 

[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.

 

[Feynman]

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

 

[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).