1. **State the problem:** Factor the quadratic trinomial $$x^2 - 4x - 12$$. 2. **Recall the factoring formula:** For a trinomial of the form $$x^2 + bx + c$$, we look for two numbers that multiply to $$c$$ and add to $$b$$. 3. **Identify coefficients:** Here, $$a=1$$, $$b=-4$$, and $$c=-12$$. 4. **Find two numbers:** We need two numbers that multiply to $$-12$$ and add to $$-4$$. 5. **List factor pairs of $$-12$$:** - $$1$$ and $$-12$$ (sum $$-11$$) - $$-1$$ and $$12$$ (sum $$11$$) - $$2$$ and $$-6$$ (sum $$-4$$) - $$-2$$ and $$6$$ (sum $$4$$) 6. **Select the correct pair:** $$2$$ and $$-6$$ multiply to $$-12$$ and add to $$-4$$. 7. **Write the factored form:** $$x^2 - 4x - 12 = (x + 2)(x - 6)$$. 8. **Verify by expansion:** $$(x + 2)(x - 6) = x^2 - 6x + 2x - 12 = x^2 - 4x - 12$$. **Final answer:** $$(x+2)(x-6)$$