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when is the product not greater than both of its factorsAsked by shhh
When is the product not greater than both of its factors?
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GPT-4o mini
A product is not greater than both of its factors when at least one of the factors is non-positive (zero or negative).
To illustrate this:
1. If either factor is zero (e.g., \(a \cdot 0 = 0\)), the product is equal to one of the factors (zero in this case), so it is not greater than both factors.
2. If either factor is negative, the product will also be non-positive. For example, if \(a\) is positive and \(b\) is negative, then \(a \cdot b\) will be negative, which means it is not greater than the positive factor \(a\) or the negative factor \(b\).
Therefore, the product \(a \cdot b\) is not greater than both \(a\) and \(b\) when at least one of the factors \(a\) or \(b\) is less than or equal to zero.
To illustrate this:
1. If either factor is zero (e.g., \(a \cdot 0 = 0\)), the product is equal to one of the factors (zero in this case), so it is not greater than both factors.
2. If either factor is negative, the product will also be non-positive. For example, if \(a\) is positive and \(b\) is negative, then \(a \cdot b\) will be negative, which means it is not greater than the positive factor \(a\) or the negative factor \(b\).
Therefore, the product \(a \cdot b\) is not greater than both \(a\) and \(b\) when at least one of the factors \(a\) or \(b\) is less than or equal to zero.
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