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

1 Answer
bartholomew
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.

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