# Abstract Algebra Problem using the division algorithm

## 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.

## 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

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

Dick
Homework Helper

## 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.

## 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.

Dick