SOLUTION: Prove that the values of the polynomial x^3–x are divisible by 6 for whole values of x.

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Question 1129671: Prove that the values of the polynomial x^3–x are divisible by 6 for whole values of x.
Answer by ikleyn(52864) About Me  (Show Source):
You can put this solution on YOUR website!
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x^3 - x = x*(x-1)*(x+1),


so the left side is the product of three consecutive integer numbers.


Of them, at least one is a multiple of 2 and exactly one is a multiple of 3.


Hence, the product, which is x^3 - x, is divisible by 2*3 = 6.

Answered and solved.