1. **State the problem:** Factor the quadratic expression $x^2 - 12x + 20$. 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, $a=1$, $b=-12$, and $c=20$. We need two numbers that multiply to $1 \times 20 = 20$ and add to $-12$. 4. **Find the numbers:** The pairs of factors of 20 are (1,20), (2,10), (4,5). To get a sum of $-12$, both numbers must be negative: $-2$ and $-10$. 5. **Rewrite the middle term:** $$x^2 - 12x + 20 = x^2 - 2x - 10x + 20$$ 6. **Group terms:** $$= (x^2 - 2x) + (-10x + 20)$$ 7. **Factor each group:** $$= x(x - 2) - 10(x - 2)$$ 8. **Factor out the common binomial:** $$= (x - 10)(x - 2)$$ 9. **Check:** Expanding $(x - 10)(x - 2)$ gives $x^2 - 2x - 10x + 20 = x^2 - 12x + 20$, which matches the original expression. **Final answer:** $$\boxed{(x - 10)(x - 2)}$$