To determine the sign of the product \( 1732 \times (-110) \), we analyze the signs of the numbers involved:
- \( 1732 \) is positive.
- \( -110 \) is negative.
When multiplying a positive number by a negative number, the product is negative. Therefore, the sign of the product \( 1732 \times (-110) \) is negative.
Correct answer: negative