When their signs are the same.
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It may be either. If any of the integers is zero, the product will be zero. Else, if one or three of the integers is negative, the product will be negative. Otherwise, it will be positive.
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The product of two integers cannot be "positive and negative".
The rule in dividing integers is to divide the absolute values. Two positive integers or two negative integers equals positive product. If one integer is positive and the other is negative, the product is negative.
Oh, dude, let me break it down for you. If you multiply three integers, the product will be positive if all three integers are either positive or negative. If you have two negative integers and one positive integer, the product will be negative. So, like, it depends on the mix of positives and negatives, you know?