1. **State the problem:** Simplify and factor the quadratic expression $x^2 - 5x - 6$. 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. Here, $a=1$, $b=-5$, and $c=-6$. We need two numbers that multiply to $1 \times (-6) = -6$ and add to $-5$. 4. The numbers are $-6$ and $1$ because $-6 \times 1 = -6$ and $-6 + 1 = -5$. 5. Rewrite the middle term using these numbers: $$x^2 - 6x + 1x - 6$$ 6. Group terms: $$ (x^2 - 6x) + (1x - 6) $$ 7. Factor each group: $$ x(x - 6) + 1(x - 6) $$ 8. Factor out the common binomial: $$ (x - 6)(x + 1) $$ 9. **Final answer:** The factored form of $x^2 - 5x - 6$ is $$ (x - 6)(x + 1) $$