1. **State the problem:** Simplify or factor the quadratic expression $x^2 - 7x + 10$. 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 our problem:** Here, $a=1$, $b=-7$, and $c=10$. We need two numbers that multiply to $1 \times 10 = 10$ and add to $-7$. 4. **Find the numbers:** The numbers are $-5$ and $-2$ because $-5 \times -2 = 10$ and $-5 + (-2) = -7$. 5. **Write the factorization:** $$x^2 - 7x + 10 = (x - 5)(x - 2)$$ 6. **Check by expansion:** $$(x - 5)(x - 2) = x^2 - 2x - 5x + 10 = x^2 - 7x + 10$$ This confirms the factorization is correct. **Final answer:** $$x^2 - 7x + 10 = (x - 5)(x - 2)$$