Polynomial long division?

Question

What is the answer to:

2x^6y+2x^4y-x^3y+1 / x^2-x+1

Please show steps if possible.

Answer 1

2x^6y + 2x^4y - x^3y + 1 / (x^2 - x + 1)


. . . . . . . . . 2x^4y + 2x^3y - 2x^2y - 5xy - 7y
x^2 - x + 1)2x^6y . .. . . . . + 2x^4y - x^3y + 1
. . . . . . . . . 2x^6y - 2x^5y + 2x^4y
. . . . . . . . . . . . . . . 2x^5y . . . . .. . . . - x^3y + 1
. . . . . . . . . . . . . . . 2x^5y + 2x^4y + 2x^3y
. . . . . . . . . . . . . . . . . . . . - 2x^4y - 3x^3y + 1
. . . . . . . . . . . . . . . . . . . . - 2x^4y + 2x^3y - 2x^2y
- 5x^3y + 2x^2y + 1
- 5x^3y + 5x^2y - 5xy
- 7x^2y + 5xy + 1
- 7x^2y + 7xy - 7y
- 2xy + 7y + 1 remainder

2x^6y + 2x^4y - x^3y + 1 / (x^2 - x + 1) =
2x^4y + 2x^3y - 2x^2y - 5xy - 7y
- (2xy - 7y - 1) / (x^2 - x + 1)