Why is $2x^3 + x$, where $x \in \mathbb{N}$, always divisible by 3? So, do you guys have any ideas? Sorry if this might seem like dumb question, but I have asked everyone I know and we haven't got a clue.

2x3 + x = x(2x2 + 1) = x(2x2 - 2 + 3) = x[2(x + 1)(x - 1) + 3] = 3x + 2x(x + 1)(x - 1)
3x is always divisible by 3 and one of x - 1, x, x + 1 is also always divisble by 3
