when will a product be positive regardless of the number of factors? & when will a product be negative regardless of the number of factors?
When all the factors are positive.
When an odd number of factors are negative. Check my thinking.
In order to determine when a product will be positive or negative regardless of the number of factors, we need to understand the concept of positive and negative numbers and their properties.
1. Positive Product:
A product will be positive when:
- All factors are positive numbers.
or
- There is an even number of negative factors.
To determine if a product will be positive, multiply all the factors together. If the result is greater than 0, then the product is positive.
For example, if you have the factors 2, 3, and 4: 2 * 3 * 4 = 24. Since 24 is greater than 0, the product is positive.
2. Negative Product:
A product will be negative when:
- There is an odd number of negative factors.
To determine if a product will be negative, multiply all the factors together. If the result is less than 0, then the product is negative.
For example, if you have the factors -2, 3, and -4: (-2) * 3 * (-4) = 24. Since 24 is not less than 0, the product is not negative.
So, regardless of the number of factors, a product will be positive if all the factors are positive, or when there is an even number of negative factors. Conversely, a product will be negative when there is an odd number of negative factors.