prove that the polynomial x^3 - x is divisible by 6 for whole number values of x

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naetonwoyev2 naetonwoyev2 · Answer 1 · 2024-02-04T03:48:16+01:00

Answer:

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.

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