SOLUTION: This is from a worksheet. I do not understand how to do this at all. I have notes from my instructor but they are not very clear to me about this type of problem. The directions ar

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: This is from a worksheet. I do not understand how to do this at all. I have notes from my instructor but they are not very clear to me about this type of problem. The directions ar      Log On


   

Question 86699: This is from a worksheet. I do not understand how to do this at all. I have notes from my instructor but they are not very clear to me about this type of problem. The directions are as follows: "Find all the real number solutions for each equation." Here is my first equation.
x^5-x=0
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
Factor, factor, factor...

x^5-x=0 factors into x(x^4-1)=0 ... so x=0 is one solution

x^4-1=0 factors into (difference of 2 squares) (x^2+1)(x^2-1)=0

x^2-1=0 factors into (x+1)(x-1)=0 ... so x=-1 and x=1 are solutions

x^2+1=0 ... x^2=-1 ... no real solutions