Abstract Algebra Problem using the division algorithm

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Homework Help Overview

The problem involves applying the division algorithm for polynomials to determine the quotient and remainder when dividing a polynomial by another polynomial in the context of Z7.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to find the quotient and remainder for a polynomial division problem and seeks validation of their results. Some participants question the correctness of the original problem statement and the calculations provided. Others suggest checking the results by verifying the multiplication of the quotient and divisor with the addition of the remainder.

Discussion Status

The discussion is ongoing, with participants providing feedback on the attempts made. There is recognition of potential errors in the calculations, and some guidance has been offered to verify the results through multiplication and addition.

Contextual Notes

Participants are working under the constraints of Z7, which may affect their calculations and interpretations of the polynomial division.

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.
 
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Are you sure the problem you wrote isn't wrong?
 
xcr said:

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.
 
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.
 
xcr said:
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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