1. **State the problem:** Simplify or factor the quadratic expression $x^2 - 13x + 12$. 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, $a=1$, $b=-13$, and $c=12$. We need two numbers that multiply to $1 \times 12 = 12$ and add to $-13$. 4. The numbers are $-1$ and $-12$ because $-1 \times -12 = 12$ and $-1 + (-12) = -13$. 5. Rewrite the middle term using these numbers: $$x^2 - x - 12x + 12$$ 6. Group terms: $$(x^2 - x) - (12x - 12)$$ 7. Factor each group: $$x(x - 1) - 12(x - 1)$$ 8. Factor out the common binomial: $$(x - 1)(x - 12)$$ **Final answer:** The factored form of $x^2 - 13x + 12$ is $$ (x - 1)(x - 12) $$.