Factor Quadratic A1E835

1. **State the problem:** Factor the quadratic expression $x^2 - 7x + 10$. 2. **Recall the factoring formula:** For a quadratic $x^2 + bx + c$, we look for two numbers that multiply to $c$ and add to $b$. 3. **Identify $b$ and $c$:** Here, $b = -7$ and $c = 10$. 4. **Find two numbers:** We need two numbers whose product is $10$ and sum is $-7$. 5. **Check factor pairs of 10:** $(1, 10)$, $(2, 5)$. 6. **Check sums:** $1 + 10 = 11$, $2 + 5 = 7$. 7. **Adjust signs:** Since sum is $-7$, both numbers must be negative: $-2$ and $-5$. 8. **Write factors:** $(x - 2)(x - 5)$. 9. **Verify by expansion:** $$ (x - 2)(x - 5) = x^2 - 5x - 2x + 10 = x^2 - 7x + 10 $$ 10. **Match with options:** The equivalent factorization is $(x - 5)(x - 2)$. **Final answer:** $(x - 5)(x - 2)$