To solve the problem of selecting the correct statement regarding integers, let's analyze each statement one by one.
### Step 1: Analyze Statement One
**Statement 1:** If the dividend and divisor are both positive, then the quotient will be negative.
- **Analysis:** This statement is incorrect. If both the dividend and divisor are positive, the quotient will also be positive. For example, \( 6 \div 2 = 3 \) (positive).
**Hint:** Remember that dividing two positive numbers always results in a positive quotient.
### Step 2: Analyze Statement Two
**Statement 2:** If two factors of a number have the same sign, their product will always be positive.
- **Analysis:** This statement is correct. If both factors are positive, the product is positive (e.g., \( 2 \times 3 = 6 \)). If both factors are negative, the product is also positive (e.g., \( -2 \times -3 = 6 \)). Therefore, the product of two factors with the same sign is always positive.
**Hint:** Multiplying two numbers with the same sign (both positive or both negative) gives a positive result.
### Step 3: Analyze Statement Three
**Statement 3:** If the addends have the same sign, the sign of the sum is the sign of the addends.
- **Analysis:** This statement is correct. If you add two positive numbers, the result is positive (e.g., \( 2 + 3 = 5 \)). If you add two negative numbers, the result is negative (e.g., \( -2 + -3 = -5 \)). Thus, the sign of the sum matches the sign of the addends.
**Hint:** Adding numbers with the same sign results in a sum that retains that sign.
### Step 4: Analyze Statement Four
**Statement 4:** All of the above statements are correct.
- **Analysis:** Since Statement One is incorrect, this statement is also incorrect.
**Hint:** Review each statement carefully to determine if they are all true before concluding.
### Conclusion
Based on the analysis:
- **Statement 1:** Incorrect
- **Statement 2:** Correct
- **Statement 3:** Correct
- **Statement 4:** Incorrect (since not all statements are correct)
### Final Answer
The correct statements are Statement 2 and Statement 3. Therefore, the correct answer is that Statements 2 and 3 are correct, while Statement 1 is incorrect, and Statement 4 is also incorrect.
