1. **State the problem:** Find the remainder when the polynomial $$x^4 + 2x^2 - 3x + 7$$ is divided by $$x + 2$$. 2. **Formula used:** According to the Remainder Theorem, the remainder of a polynomial $$f(x)$$ divided by $$x - a$$ is $$f(a)$$. 3. **Apply the theorem:** Here, the divisor is $$x + 2$$, which can be rewritten as $$x - (-2)$$, so $$a = -2$$. 4. **Evaluate the polynomial at $$x = -2$$:** $$f(-2) = (-2)^4 + 2(-2)^2 - 3(-2) + 7$$ 5. **Calculate each term:** $$(-2)^4 = 16$$ $$2(-2)^2 = 2 \times 4 = 8$$ $$-3(-2) = 6$$ 6. **Sum all terms:** $$16 + 8 + 6 + 7 = 37$$ 7. **Conclusion:** The remainder is $$37$$. **Final answer:** 37