Three negative integers and one positive integer are multiplied. Find the sign of the product.

Options

A. positive integer
B. negative integer
C. cannot be determined
D. none of the above

Answer

To determine the sign of the product of three negative integers and one positive integer, we can follow these steps:

### Step 1: Identify the integers
Let's assume the three negative integers are -2, -3, and -4, and the positive integer is 5.

### Step 2: Understand the multiplication rules for signs
- The product of two negative integers is positive.
- The product of a negative integer and a positive integer is negative.
- The product of two positive integers is positive.

### Step 3: Multiply the negative integers first
Multiply the first two negative integers:
\[ -2 \times -3 = 6 \quad (\text{positive}) \]

### Step 4: Multiply the result with the third negative integer
Now, multiply the result (6) with the third negative integer (-4):
\[ 6 \times -4 = -24 \quad (\text{negative}) \]

### Step 5: Multiply the result with the positive integer
Finally, multiply the result (-24) with the positive integer (5):
\[ -24 \times 5 = -120 \quad (\text{negative}) \]

### Conclusion
The final product is -120, which is negative. Therefore, the sign of the product of three negative integers and one positive integer is **negative**.

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