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August 27th, 2013, 02:11 AM  #1 
Senior Member Joined: Sep 2010 From: Oslo, Norway Posts: 162 Thanks: 2  Rewrite polynomial*2x as a sum of polynomial
Hello there, I have a polynomial Pn(x) multiplied by 2x: . I want to rewrite it as a sum like this: I realize I can do this at least one way: . However, I want to know if there is a simpler way to write it, ideally an expression which is easy to manipulate algebraically. Thank you for helping me learn mathematics. Kind regards, Marius 
August 27th, 2013, 02:45 AM  #2 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 879 Thanks: 60 Math Focus: सामान्य गणित  Re: Rewrite polynomial*2x as a sum of polynomial
Why do u want to write in more simpler form ?

August 27th, 2013, 02:53 AM  #3 
Senior Member Joined: Sep 2010 From: Oslo, Norway Posts: 162 Thanks: 2  Re: Rewrite polynomial*2x as a sum of polynomial
Because I want to prove an equation by induction. I assume that the case is true for , In the case of I want to separate out the from . The most difficult way I could achieve this was in trying rewrite my lefthand side as a sum of 2x times, or some easily manipulable object. Thank you for your time. Kind regards, Marius 
August 27th, 2013, 02:55 AM  #4  
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Re: Rewrite polynomial*2x as a sum of polynomial Quote:
lets say the grade of is a. Then the grade of is equal to a+1. But if you say the last is equal to the sum of then the grade remains a. since a is not the same as a+1 That was wrong I think.  
August 27th, 2013, 05:13 AM  #5  
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: Rewrite polynomial*2x as a sum of polynomial Quote:
 
August 27th, 2013, 05:30 AM  #6  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,898 Thanks: 1093 Math Focus: Elementary mathematics and beyond  Re: Rewrite polynomial*2x as a sum of polynomial Quote:
 
August 27th, 2013, 07:11 AM  #7  
Global Moderator Joined: Dec 2006 Posts: 20,089 Thanks: 1902  Quote:
 

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