How do you long divide (x^2 - xy + y^2) /( x+y)?

1 Answer
May 21, 2018

(x+y) does not divide (x^2-xy+y^2).

Explanation:

You will notice that

(x+y)(x-2y)+3y^2=x^2-xy+y^2

so in a sense, (x+y) divides (x^2-xy+y^2) by (x-2y) with a remainder of 3y^2, but this is not how a remainder is defined in polynomial long division. I don't believe Socratic supports writing long division, but I can link you to the wikipedia page on polynomial long division. Please comment if you have any questions.