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

  • Context: High School 
  • Thread starter Thread starter Feynman
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the factorization of the polynomial X^4 + X^3 + X^2 + X + 1. Participants explore various approaches to factorizing the polynomial, including multiplication by (x-1) and considerations of complex numbers and roots of unity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asks how to factorize the polynomial X^4 + X^3 + X^2 + X + 1.
  • Another participant suggests multiplying the polynomial by (x-1) as a potential method for factorization.
  • There is a request for clarification on how to multiply the polynomial by (x-1) to achieve factorization.
  • Some participants express frustration at not receiving a detailed step-by-step explanation for the factorization process.
  • A later reply indicates that the polynomial can be related to X^5 - 1 and suggests exploring complex numbers and roots of unity for further insights.
  • It is noted that 1 is not a root of the polynomial due to the multiplication by (x-1).

Areas of Agreement / Disagreement

Participants do not reach a consensus on the factorization method, with multiple competing views and approaches presented throughout the discussion.

Contextual Notes

Some participants express uncertainty about the multiplication process and the implications of using complex numbers and roots of unity in the factorization.

Feynman
Messages
152
Reaction score
0
Hello ,
how to factorize the folowing polynomial[tex]X^4+X^3+X^2+X+1[/tex]
 
Mathematics news on Phys.org
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 [itex]e^{i \theta}[/itex], 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:

Similar threads

High School About a definition: What is the number of terms of a polynomial P(x)?
  • · Replies 48 ·
2
Replies
48
Views
5K
MHB Can you factor the following two polynomials?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
  • · Replies 16 ·
Replies
16
Views
2K
MHB Factorize 6(x^5+y^5+z^5)-5(x^2+y^2+z^2)(x^3+y^3+z^3)
  • · Replies 1 ·
Replies
1
Views
1K
High School Strange quadratic manipulation
  • · Replies 6 ·
Replies
6
Views
2K
MHB How can you solve $5^{x^2+8}=125^{2x}$ for x?
  • · Replies 8 ·
Replies
8
Views
1K
MHB Solve Equation: $x^4+2x^3-x^2-6x-3=0$
  • · Replies 7 ·
Replies
7
Views
2K
High School What went wrong with (-x)^2=x^2?
  • · Replies 22 ·
Replies
22
Views
3K
MHB -s6.6 solve exponential eq 3^x-14\cdot 3^{-x}=5
  • · Replies 1 ·
Replies
1
Views
1K
High School Complete the square, yes, but what does it mean?
  • · Replies 19 ·
Replies
19
Views
4K