1. **State the problem:** Factorize the quadratic expression $x^2 - x - 6$. 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. **Apply to the problem:** Here, $a=1$, $b=-1$, and $c=-6$. We need two numbers that multiply to $1 \times (-6) = -6$ and add to $-1$. 4. **Find the numbers:** The numbers are $2$ and $-3$ because $2 \times (-3) = -6$ and $2 + (-3) = -1$. 5. **Rewrite the middle term:** $$x^2 - x - 6 = x^2 + 2x - 3x - 6$$ 6. **Group terms:** $$= (x^2 + 2x) - (3x + 6)$$ 7. **Factor each group:** $$= x(x + 2) - 3(x + 2)$$ 8. **Factor out the common binomial:** $$= (x - 3)(x + 2)$$ **Final answer:** $(x-3)(x+2)$