
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 18th, 2015, 07:21 AM  #1 
Newbie Joined: Jan 2013 Posts: 12 Thanks: 0  Factorising Higher Order Polynomials.
POSTED AGAIN IN THIS FORUM AS INCORRECTLY POSTED IN HIGH SCHOOL MATH Can somebody explain to me the "rule" for factorising this polynomial: s^5 + 2s^4 + 4s^3 +8s^2 +10s +6 It was explained to me some time ago that that doubling coefficients 1,2,4 and 8 is a "special" format that would allow me to solve this fairly easily. However, I do not remember. Also, for general knowledge, are there other types of high order polynomial like this with special formats that can be solved easily? It's been suggested these types of higher order polynomials could be part of exam problems in vibration and control module. Thanks. Last edited by skipjack; April 18th, 2015 at 05:07 PM. 
April 18th, 2015, 05:47 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,924 Thanks: 2203 
There isn't such a rule. If all the coefficients conformed to that pattern, it would be a different matter.

April 20th, 2015, 10:38 AM  #3 
Senior Member Joined: Nov 2010 From: Berkeley, CA Posts: 174 Thanks: 35 Math Focus: Elementary Number Theory, Algebraic NT, Analytic NT 
Perhaps you are thinking of Eisenstein's criterion. We see that your polynomial is irreducible over the rationals by applying that rule with p = 2


Tags 
factorising, higher, order, polynomials 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Factorising Higher Order Polynomials.  MMCS  Algebra  2  April 18th, 2015 08:45 AM 
Factorising polynomials  juxhin  Elementary Math  3  November 24th, 2013 07:52 AM 
factorising reducible polynomials  miahmad  Calculus  1  June 7th, 2010 05:14 PM 
How do you find the roots of polynomials that go higher then  wonger357  Algebra  1  April 30th, 2009 03:59 AM 
Factorising cubic polynomials through short division  Voltman  Algebra  2  April 9th, 2009 06:14 AM 