Two negative integers and one positive integer are being 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 when multiplying two negative integers and one positive integer, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Integers**: Let's denote the two negative integers as \( x \) and \( y \), and the positive integer as \( z \). So we have:
- \( x < 0 \) (negative integer)
- \( y < 0 \) (negative integer)
- \( z > 0 \) (positive integer)

2. **Multiply the Two Negative Integers**: When we multiply two negative integers, the result is positive. Therefore, we calculate:
\[ x \times y = -x \times -y = + (xy) \]
This means the product of \( x \) and \( y \) is a positive integer.

3. **Multiply the Result with the Positive Integer**: Now, we take the positive result from the previous step and multiply it by the positive integer \( z \):
\[ (xy) \times z = + (xy) \times +z = + (xyz) \]
Since both \( xy \) and \( z \) are positive, their product will also be positive.

4. **Conclusion**: The final product of multiplying two negative integers and one positive integer is positive.

### Final Answer:
The sign of the product is **positive**.