Is the product `-12xx-15xx3xx4xx5xx-2` positive or negative?

Answer

To determine whether the product \(-12 \times -15 \times 3 \times 4 \times 5 \times -2\) is positive or negative, we can analyze the signs of the numbers involved in the multiplication.

### Step-by-step Solution:

1. **Identify the signs of each number:**
- \(-12\) (negative)
- \(-15\) (negative)
- \(3\) (positive)
- \(4\) (positive)
- \(5\) (positive)
- \(-2\) (negative)

2. **Count the number of negative numbers:**
- There are 3 negative numbers: \(-12\), \(-15\), and \(-2\).

3. **Determine the sign of the product based on the number of negative factors:**
- The rule is:
- An even number of negative factors results in a positive product.
- An odd number of negative factors results in a negative product.
- Since we have 3 negative numbers (which is odd), the product will be negative.

4. **Combine the positive numbers:**
- The positive numbers are \(3\), \(4\), and \(5\).
- The product of these positive numbers is \(3 \times 4 \times 5\), which is positive.

5. **Combine the results:**
- We have a positive product from the positive numbers and a negative product from the negative numbers.
- Therefore, the overall product is positive (from the positive numbers) multiplied by negative (from the negative numbers), resulting in a negative product.

### Conclusion:
The product \(-12 \times -15 \times 3 \times 4 \times 5 \times -2\) is **negative**.

---