1. **State the problem:** Factor the quadratic expression $$x^2 - 3x - 4$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, we look for two numbers that multiply to $$ac$$ and add to $$b$$. 3. **Identify coefficients:** Here, $$a=1$$, $$b=-3$$, and $$c=-4$$. 4. **Calculate product and sum:** We need two numbers that multiply to $$1 \times (-4) = -4$$ and add to $$-3$$. 5. **Find the numbers:** The numbers are $$-4$$ and $$1$$ because $$-4 \times 1 = -4$$ and $$-4 + 1 = -3$$. 6. **Rewrite the middle term:** $$x^2 - 4x + 1x - 4$$. 7. **Group terms:** $$(x^2 - 4x) + (1x - 4)$$. 8. **Factor each group:** $$x(x - 4) + 1(x - 4)$$. 9. **Factor out the common binomial:** $$(x - 4)(x + 1)$$. 10. **Final answer:** The factored form of $$x^2 - 3x - 4$$ is $$\boxed{(x - 4)(x + 1)}$$.