Determine if each product is positive, negative, or zero. Do not compute. Explain why on your paper. a. \( (-30)(-38)(-97)(-38)(-70)(20) \) : positive negative zero b. \( (50)(-58)(-94)(-22)(2)(17) \) : positive negative zero c. \( (-91)(-28)(16)(0)(-69)(-24) \) : positive negative dero d. \( (39)(-57)(-11)(-5)(97)(-28) \) : positive negative zero e. \( (-79)(-39)(-88)(-27)(-80)(-50) \) : positive negative zero Submit Ouestion

Certainly! Let's analyze each product to determine whether it's positive, negative, or zero without performing the actual multiplication. --- ### a. \( (-30)(-38)(-97)(-38)(-70)(20) \) - **Zero Check:** None of the factors are zero. - **Negative Factors Count:** There are **5 negative numbers**: -30, -38, -97, -38, -70. - **Sign Determination:** - An **odd** number of negative factors results in a **negative** product. **Answer:** **Negative** --- ### b. \( (50)(-58)(-94)(-22)(2)(17) \) - **Zero Check:** None of the factors are zero. - **Negative Factors Count:** There are **3 negative numbers**: -58, -94, -22. - **Sign Determination:** - An **odd** number of negative factors results in a **negative** product. **Answer:** **Negative** --- ### c. \( (-91)(-28)(16)(0)(-69)(-24) \) - **Zero Check:** One of the factors is **0**. - **Sign Determination:** - **Any** product that includes a zero is **zero**. **Answer:** **Zero** --- ### d. \( (39)(-57)(-11)(-5)(97)(-28) \) - **Zero Check:** None of the factors are zero. - **Negative Factors Count:** There are **4 negative numbers**: -57, -11, -5, -28. - **Sign Determination:** - An **even** number of negative factors results in a **positive** product. **Answer:** **Positive** --- ### e. \( (-79)(-39)(-88)(-27)(-80)(-50) \) - **Zero Check:** None of the factors are zero. - **Negative Factors Count:** There are **6 negative numbers**: -79, -39, -88, -27, -80, -50. - **Sign Determination:** - An **even** number of negative factors results in a **positive** product. **Answer:** **Positive** --- **Summary of Answers:** - **a. Negative** - **b. Negative** - **c. Zero** - **d. Positive** - **e. Positive** --- **Explanation Summary:** To determine the sign of the product: 1. **Check for Zero:** If any factor is zero, the entire product is zero. 2. **Count Negative Factors:** - **Odd Number of Negatives:** Product is negative. - **Even Number of Negatives:** Product is positive. By applying these rules to each set of factors, we can determine the sign of each product without actual computation.