Question

Show that x + y is a factor of x ^5 + y^5 and x ^7 + y^7 . By using synthetic division, find the quotient in each case. 

Answer 1

$\frac{x^5+y^5}{x+y}=x^4-x^3y+x^2y^2-xy^3+y^4.$

$\frac{x^7+y^7}{x+y}=x^6-x^5y+x^4y^2-x^3y^3+x^2y^4-xy^5+y^6.$