Question

(Divide the following polynomials (x5 + y5) ÷ (x + y)

Answer 1

`\text{Use}\ a^5+b^5=(a + b) (a^4 - a^3 b + a^2 b^2 - a b^3 + b^4).\\\\(x^5+y^5):(x+y)=(x^5+y^5)/(x+y)=((x+y)(x^4-x^3y+x^2y^2-xy^3+y^4))/(x+y)\\\\=\boxed{x^4-x^3y+x^2y^2-xy^3+y^4}`