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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: 20,622 Thanks: 2074 
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


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