1. **State the problem:** Factor the quadratic expression $g^2 + 12g - 13$. 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. **Identify coefficients:** Here, $a=1$, $b=12$, and $c=-13$. 4. **Calculate product $ac$:** $$ac = 1 \times (-13) = -13$$ 5. **Find two numbers that multiply to $-13$ and add to $12$:** These numbers are $13$ and $-1$ because $13 \times (-1) = -13$ and $13 + (-1) = 12$. 6. **Rewrite the middle term using these numbers:** $$g^2 + 13g - 1g - 13$$ 7. **Group terms:** $$(g^2 + 13g) + (-1g - 13)$$ 8. **Factor each group:** $$g(g + 13) - 1(g + 13)$$ 9. **Factor out the common binomial:** $$(g - 1)(g + 13)$$ **Final answer:** The factored form of $g^2 + 12g - 13$ is $$\boxed{(g - 1)(g + 13)}$$