1. Stating the problem: We want to find the remainder when the cubic polynomial $$f(x) = 2x^3 - x^2 + 2x - 16$$ is divided by $$x + 5$$. 2. According to the Remainder Theorem, the remainder of dividing $$f(x)$$ by $$x - a$$ is $$f(a)$$. Here, we have $$x + 5 = x - (-5)$$, so $$a = -5$$. 3. Evaluate $$f(-5)$$: $$f(-5) = 2(-5)^3 - (-5)^2 + 2(-5) - 16$$ $$= 2(-125) - 25 - 10 - 16$$ $$= -250 - 25 - 10 - 16$$ $$= -301$$. 4. Therefore, the remainder when $$f(x)$$ is divided by $$x + 5$$ is $$-301$$.