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If x is an integer, then (x3 - x) is always divisible by which number?
- A4
- B6
- C8
- D9
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CCommunity
Then, (x3 - x) = x(x2 - 1)
(x2 - 1) is divisible by 2 or 3.
2 and 3 are factors of 6.
For example:
If n = 3, then
(x3 - x) = (27 - 3) = 24
Factors of 24 is 24, 12, 8, 6, 3, 2 and 1.
∴ (x3 - x) is always divisible by 6.
(x2 - 1) is divisible by 2 or 3.
2 and 3 are factors of 6.
For example:
If n = 3, then
(x3 - x) = (27 - 3) = 24
Factors of 24 is 24, 12, 8, 6, 3, 2 and 1.
∴ (x3 - x) is always divisible by 6.