The signs of the terms are + - + -, so there are 3 changes of sign. By Descartes' rule of signs, that means there are 3 (or 1) positive real roots. It also means there are

The derivative is

F'(x) = 6x^2 - 8x + 8

The discriminant of this expression is (-8)^2 - 4(6)(8) = 64 - 192 = -128.

This means the derivative expression F'(x) is positive for all values of x, so the slope of the expression F(x) is positive for all values of x. There will be 2 imaginary zeros of F(x).

Here's the graph of F(x).

**0 or 2 possible imaginary roots**.The derivative is

F'(x) = 6x^2 - 8x + 8

The discriminant of this expression is (-8)^2 - 4(6)(8) = 64 - 192 = -128.

This means the derivative expression F'(x) is positive for all values of x, so the slope of the expression F(x) is positive for all values of x. There will be 2 imaginary zeros of F(x).

Here's the graph of F(x).