1. **State the problem:** Simplify or factor the quadratic expression $x^2 + x - 12$. 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, $a=1$, $b=1$, and $c=-12$. We need two numbers that multiply to $1 \times (-12) = -12$ and add to $1$. 4. The numbers $4$ and $-3$ satisfy this because $4 \times (-3) = -12$ and $4 + (-3) = 1$. 5. Rewrite the middle term using these numbers: $$x^2 + 4x - 3x - 12$$ 6. Group terms: $$(x^2 + 4x) - (3x + 12)$$ 7. Factor each group: $$x(x + 4) - 3(x + 4)$$ 8. Factor out the common binomial: $$(x - 3)(x + 4)$$ **Final answer:** The factored form of $x^2 + x - 12$ is $$(x - 3)(x + 4)$$.