find out the remainder when x+x^9+x^25+x^49+x^81 divided by x^2-x

Dear Student

Here is the solution of question you have posted

Let P(x) = x+x^9+x^25+x^49+x^81 = x(1+x⁸+x²⁴+x⁴⁸+x⁸⁰)

and Q(X)= x(x-1)

Now When P(x) is divided by Q(X) then x is common factor which cancels out so

remainder when  say S(x)= (1+x⁸+x²⁴+x⁴⁸+x⁸⁰) is divided by R(x)= (x-1) using remainder theorem is S(1)= 5

Hope it clarifies your doubt

Regards

Team Topperlearning