1. **State the problem:** Simplify or factor the quadratic expression $x^2 - 13x + 42$. 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, $a=1$, $b=-13$, and $c=42$. We need two numbers that multiply to $42$ and add to $-13$. 4. **Find the numbers:** The pair is $-6$ and $-7$ because $-6 \times -7 = 42$ and $-6 + (-7) = -13$. 5. **Write the factored form:** $$x^2 - 13x + 42 = (x - 6)(x - 7)$$ 6. **Explanation:** Factoring breaks the quadratic into two binomials whose product gives the original expression. This helps solve equations or analyze the function. **Final answer:** $(x - 6)(x - 7)$