Question

What is the sign of the product \( (8)(-23)(-21)(-29) \)? a. Negative, because the product \( (8)(-23) \) is positive and \( (-21)(-29) \) is negative. b. Positive, because \( (8)(-23) \) and \( (-21)(-29) \) are positive. c. Positive, because \( (8)(-23) \) and \( (-21)(-29) \) are negative. d. Negative, because \( (8)(-23) \) is negative and \( (-21)(-29) \) is positive.

Answer 1

The product (8)(-23)(-21)(-29) is negative because there are three negative factors and one positive factor, resulting in an overall negative product.

The correct answer to the given question is: d.

Step-by-step explanation:

The sign of the product (8)(-23)(-21)(-29) can be determined by understanding the rules of multiplying numbers with different signs. According to the multiplication rules, when two positive numbers are multiplied together, the result is positive. Similarly, when two negative numbers are multiplied together, the result is also positive. However, when a positive number and a negative number are multiplied together, the result is negative. Applying these rules to the given product:

• (8)(-23) results in a negative product because a positive number is being multiplied by a negative number.
• (-21)(-29) results in a positive product because two negative numbers are being multiplied together.

Therefore, the product (8)(-23)(-21)(-29) overall has three negative factors and one positive factor. Since there is an odd number of negative factors, the product will be negative.

The correct answer to the given question is:

d. Negative, because (8)(-23) is negative and (-21)(-29) is positive.