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Chapter 1: Problem 149

Think About It A nonzero product has 25 factors, 17 of which are negative. What is the sign of the product? Explain.

Short Answer

Expert verified
The sign of the product is negative.

Step by step solution

01

Understand the Multiplication Rule for Negative Numbers

In multiplication, negative numbers follow specific rules. Multiplying two negative numbers yields a positive result, implying that any even number of negative numbers multiplied together will also result in a positive product. A negative result occurs when an odd number of negative numbers are multiplied together.
02

Assign Sign based on Number of Negative Factors

There are 17 negative factors in the product. Since there are an odd number of negative numbers, by the rule of negative number multiplication, the product will be negative.
03

Finalize the Sign of the Product

Regardless of the other eight variables, the product's sign is solely determined by the 17 negative factors. Since an odd number of negative factors will result in a negative product, the product in this scenario is negative.

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