Final answer:
The sign of a nonzero product with 25 factors, 17 of which are negative, is negative. This is because an odd number of negative factors results in a negative product.
Step-by-step explanation:
If a nonzero product has 25 factors, 17 of which are negative, we must determine the sign of the product. Multiplication rules indicate that when two positive numbers are multiplied, their product is positive, and when two negative numbers are multiplied, their product is also positive. However, when a positive and a negative number are multiplied, the product is negative. Since there are an odd number of factors (17) that are negative, we would have an unpaired negative factor after grouping negative factors in pairs. Multiplying these pairs results in a positive product, but multiplying the last unpaired negative factor will give a final product that is negative. Thus, the sign of the product with an odd number of negative factors will also be negative. Consequently, the product will be negative.