Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you divide # (x^5 + y^5) /(x + y)#?

1 Answer

Konstantinos Michailidis

Mar 7, 2016

For #n# odd integer the following identity holds

#x^n + y^n = (x + y)(x^{n-1} - x^{n-2}y + \cdots - xy^{n-2} + y^{n-1} )#

or

#[x^n + y^n]/[x+y]=(x^{n-1} - x^{n-2}y + \cdots - xy^{n-2} + y^{n-1} )#

Hence for our case we have that

#[x^5+y^5]/[x+y]=x^4-x^3 y+x^2 y^2-x y^3+y^4#

Related questions

See all questions in Long Division of Polynomials

Impact of this question

27039 views around the world

You can reuse this answer
Creative Commons License