1. **State the problem:** Factor the quadratic polynomial $$x^2 + 4x - 12$$ completely. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two numbers that multiply to $$ac$$ and add to $$b$$. 3. **Apply to the problem:** Here, $$a=1$$, $$b=4$$, and $$c=-12$$. 4. **Find two numbers:** We need two numbers that multiply to $$1 \times (-12) = -12$$ and add to $$4$$. These numbers are $$6$$ and $$-2$$ because $$6 \times (-2) = -12$$ and $$6 + (-2) = 4$$. 5. **Rewrite the middle term:** $$x^2 + 6x - 2x - 12$$. 6. **Group terms:** $$(x^2 + 6x) + (-2x - 12)$$. 7. **Factor each group:** $$x(x + 6) - 2(x + 6)$$. 8. **Factor out the common binomial:** $$(x - 2)(x + 6)$$. 9. **Final answer:** The completely factored form is $$\boxed{(x + 6)(x - 2)}$$.