1. **State the problem:** Simplify and factor the quadratic expression $x^2 - 2x - 8$. 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. Here, $a=1$, $b=-2$, and $c=-8$. We need two numbers that multiply to $1 \times (-8) = -8$ and add to $-2$. 4. The numbers are $-4$ and $2$ because $-4 \times 2 = -8$ and $-4 + 2 = -2$. 5. Rewrite the middle term using these numbers: $$x^2 - 4x + 2x - 8$$ 6. Group terms: $$(x^2 - 4x) + (2x - 8)$$ 7. Factor each group: $$x(x - 4) + 2(x - 4)$$ 8. Factor out the common binomial: $$(x - 4)(x + 2)$$ **Final answer:** $$x^2 - 2x - 8 = (x - 4)(x + 2)$$