Factoring Problem

[Birdsy]

I need to factor this completely:

x^5-x=0

I started with x (x^4-1)=0
then x (x^2+1) (x^2-1)=0
then x (x^2+1) (x+1) (x-1)=0

I thought that last one was right, but the online textbook says it should look like this:

x(x-1)(x^3+1x^2+1x+1) = 0

I don't see how they got that. Help!

 

[Denis]

Obvious that x = 1; 1^5 - 1 = 1 - 1 = 0
What are you trying to do?

 

[wjm11]

factor this completely:

x^5-x=0

I started with x (x^4-1)=0
then x (x^2+1) (x^2-1)=0
then x (x^2+1) (x+1) (x-1)=0

I thought that last one was right, but the online textbook says it should look like this:

x(x-1)(x^3+1x^2+1x+1) = 0

Your solution is correct. The textbook answer is not completely factored.

(x^3+1x^2+1x+1) = (x^2+1) (x+1)

Solutions to the equation are x = 1 or -1 or 0

 

[Denis]

Good nuff Arthur; but that's really the solution to x^(2n+1) - x, right?