1. **State the problem:** Find the remainder when the polynomial $$f(x) = 2x^5 - 5x^2 + 2$$ is divided by $$x + 3$$. 2. **Recall the Remainder Theorem:** When a polynomial $$f(x)$$ is divided by $$x - a$$, the remainder is $$f(a)$$. 3. **Rewrite divisor:** Here, the divisor is $$x + 3$$, which can be written as $$x - (-3)$$. So, $$a = -3$$. 4. **Evaluate $$f(-3)$$:** $$ \begin{aligned} f(-3) &= 2(-3)^5 - 5(-3)^2 + 2 \\ &= 2(-243) - 5(9) + 2 \\ &= -486 - 45 + 2 \\ &= -529. \end{aligned} $$ 5. **Conclusion:** The remainder when $$f(x)$$ is divided by $$x + 3$$ is $$-529$$.