Abstract Algebra Problem using the division algorithm

  • Thread starter xcr
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  • #1
xcr
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Homework Statement



Apply the division algorithm for polynomials to find the quotient and remainder when (x^4)-(2x^3)+(x^2)-x+1 is divided by (2x^2)+x+1 in Z7.


Homework Equations





The Attempt at a Solution



I worked the problem and got that the quotient was (4x^2)-3x-1 and the remainder was 4x+2. Are these right? If not then some help would be appreciated.
 

Answers and Replies

  • #2
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Are you sure the problem you wrote isn't wrong?
 
  • #3
Dick
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Homework Statement



Apply the division algorithm for polynomials to find the quotient and remainder when (x^4)-(2x^3)+(x^2)-x+1 is divided by (2x^2)+x+1 in Z7.


Homework Equations





The Attempt at a Solution



I worked the problem and got that the quotient was (4x^2)-3x-1 and the remainder was 4x+2. Are these right? If not then some help would be appreciated.

No, I don't think so. But it's close enough that you understand what you are doing and probably just made a mechanical error. You can check your answer by multiplying 2x^2+x+1 times your quotient and adding the remainder and seeing if you get the original polynomial.
 
  • #4
xcr
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Ok, I think I got it now. I got the quotient is (4x^2)-3x and the remainder is 2x+1. I multiplied the quotient and (2x^2)+x+1 and added the remainder and it came to the original polynomial. Thanks for checking over my work.
 
  • #5
Dick
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Ok, I think I got it now. I got the quotient is (4x^2)-3x and the remainder is 2x+1. I multiplied the quotient and (2x^2)+x+1 and added the remainder and it came to the original polynomial. Thanks for checking over my work.

Closer. Is there another error or did you just mistype the remainder?
 

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