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

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To factorize the polynomial X^4 + X^3 + X^2 + X + 1, it is suggested to multiply it by (x - 1). This approach leads to the expression X^5 - 1, which can be analyzed using complex numbers and roots of unity. The discussion emphasizes that the polynomial has five roots, but notes that 1 is not a root due to the multiplication. Participants are encouraged to explore the polynomial's properties further, particularly through complex analysis. Understanding these concepts is essential for successful factorization.
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Hello ,
how to factorize the folowing polynomialX^4+X^3+X^2+X+1
 
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Multiply by (x-1).
 
StatusX said:
Multiply by (x-1).

How please?
can you clarify?
 
What do you mean how? Just multiply the polynomial by (x-1) and see what you get.
 
StatusX said:
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
 
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.
 
I Arrivided To X^5-1
So How To Factorise It?
 
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).
 
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