Homework Help: Abstract Algebra Problem using the division algorithm

1. Dec 10, 2011

xcr

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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.

2. Dec 10, 2011

mtayab1994

Are you sure the problem you wrote isn't wrong?

3. Dec 10, 2011

Dick

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. Dec 10, 2011

xcr

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. Dec 10, 2011

Dick

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