Question

What is the remainder when x+x9+x25+x49+x81 is divided by x3-x ?

Answer 1

x+9x+25x+49x+81x÷ 3x-x

=165x÷3x-x

=165x÷x(3-1)

=165/2

=82.5
I hope this is the answer

Answer 2

Step by step statement:

x^3 -x=0

x(x^2 -1)=0

Roots are x=0, 1,-1

x+x^9 +x^25 +x^49 +x^81

Putting x to be 0,

Remainder=0

Putting x to be 1,

Remainder=1+1+1+1+1=5

Putting x to be -1,

Remainder=-1-1-1-1-1=-5

But one factor divides the equation so x^3-x divides equation.