SOLUTION: Help me solve this polynomial equation algebraically: (x^6) - (x^2) = 0

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Question 717597: Help me solve this polynomial equation algebraically:
(x^6) - (x^2) = 0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E6+-+x%5E2+=+0...factor out x%5E2
x%5E2+%28x%5E4+-+1%29=+0.....write x%5E4+-+1 as %28x%5E2%29%5E2+-+1%5E2

x%5E2+%28%28x%5E2%29%5E2+-+1%5E2%29=+0...factor %28x%5E2%29%5E2+-+1%5E2 as %28x%5E2+-+1%29%28x%5E2%2B+1%29
x%5E2+%28%28x%5E2+-+1%29%28x%5E2%2B+1%29%29=+0...factor %28x%5E2+-+1%29 as %28x+-+1%29%28x%2B1%29

x%5E2+%28x+-+1%29%28x%2B1%29%28x%5E2%2B+1%29=+0
solutions:
if x%5E2=0.....=>...x=0
if x-1=0.....=>...x=1
if x%2B1=0.....=>...x=-1
if x%5E2%2B+1=0.....=>...x%5E2=-1.....=>...x=sqrt%28-1%29...=>...x=i or x=-i