1. **State the problem:** Factor the quadratic expression $x^2 + 16x - 36$. 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, $a=1$, $b=16$, and $c=-36$. We need two numbers that multiply to $1 \times (-36) = -36$ and add to $16$. 4. **Find the numbers:** The pair is $18$ and $-2$ because $18 \times (-2) = -36$ and $18 + (-2) = 16$. 5. **Rewrite the middle term:** $$x^2 + 18x - 2x - 36$$ 6. **Group terms:** $$(x^2 + 18x) + (-2x - 36)$$ 7. **Factor each group:** $$x(x + 18) - 2(x + 18)$$ 8. **Factor out the common binomial:** $$(x - 2)(x + 18)$$ **Final answer:** The factorization of $x^2 + 16x - 36$ is $$\boxed{(x - 2)(x + 18)}$$.