To determine the sign of the product \( 1732 \times (-110) \), we analyze the signs of the numbers involved:
- \( 1732 \) is a positive number.
- \( -110 \) is a negative number.
The product of a positive number and a negative number is always negative. Therefore, the sign of the product \( 1732 \times (-110) \) is negative.
So the correct response is: negative.