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September 13th, 2013, 11:05 AM  #1 
Newbie Joined: Sep 2013 Posts: 24 Thanks: 0  Help with polynomials
I have never solved something like this, can you please show me step by step? The polynomial P4 (x) = x4 + x3x2 + x2 is divisible by x2 +1. Enter zeros polynomial. I used google translate to translate it so please bear with me If you could comment every step as well as present all the laws/rules you were using, it would be great because I really want to learn how to solve these. 
September 13th, 2013, 11:49 AM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Help with polynomials Hello, n777l! Quote:
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September 13th, 2013, 05:12 PM  #3 
Newbie Joined: Sep 2013 Posts: 24 Thanks: 0  Re: Help with polynomials
Thank you, but what does the +i stand for? How did you come up with the zeros 1, 2 and +i just by looking at: (x1)(x+2)(x2+1)=0? 
September 13th, 2013, 06:48 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,805 Thanks: 2150 
(x  1)(x + 2)(x² + 1) = 0 The product on the lefthand side can't be zero unless one of the factors is zero. If x  1 = 0, x = 1. If x + 2 = 0, x = 2. If x² + 1 = 0, x² = 1 and so x = ?(1) or ?(1). As ?(1) is not a real number, it's convenient to use to represent it. 
September 14th, 2013, 03:13 PM  #5 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Help with polynomials
If you are not familiar with "i" then you probably are only expected to give the real number roots. But still the fact that is divisible by (and leaves ) tells you that . And since is not 0 for any real number value of x, any root must satisfy . Now, use the fact that if the product of two numbers is 0, one or both must be 0. So either x+ 2= 0 or x 1= 0. If the first is true, then x= 2, if the second is true, then x= 1. 
September 14th, 2013, 03:25 PM  #6 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Help with polynomials
If you are not familiar with "i" then you probably are only expected to give the real number roots. But still the fact that is divisible by (and leaves ) tells you that . And since is not 0 for any real number value of x, any root must satisfy . Now, use the fact that if the product of two numbers is 0, one or both must be 0. So either x+ 2= 0 or x 1= 0. If the first is true, then x= 2, if the second is true, then x= 1. 

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