Which of the following represents the factored form of f(x) = x3 − 81x?

f(x) = x(x − 9)2
f(x) = (x + 9)(x − 9)
f(x) = x(x + 9)(x − 9)
f(x) = x(x2 − 9)

You're original equation has a -81, so the factored form will have to have a positive and negative multiplying one another to achieve that...

f(x) = x(x + 9)(x - 9)

F(x) = x^3 - 81x
f(x) = x(x^2) + x(81)
f(x) = x(x^2 - 81)
f(x) = x(x^2 + 9x - 9x - 81)
f(x) = x(x(x) + x(9) - 9(x) - 9(9))
f(x) = x(x(x + 9) - 9(x + 9))
f(x) = x(x - 9)(x + 9)

The answer is C.