What determines if the product of two integers is positive, negative, or zero?

The product of two integers can be positive, negative, or zero depending on the integers involved. Here’s how it works:

• Product is Positive: When both integers are either positive or negative. For example: (3) * (4) = 12 and (-3) * (-4) = 12. In both cases, the result is a positive integer.
• Product is Negative: When one integer is positive and the other is negative. For example: (3) * (-4) = -12 and (-3) * (4) = -12. In these cases, the product is negative due to the presence of one positive and one negative integer.
• Product is Zero: When at least one of the integers is zero. For example: (0) * (5) = 0 and (3) * (0) = 0. In either situation, since one of the integers is zero, the product is zero.

In summary, the rules for determining the sign of the product of two integers are straightforward: if both are the same sign, the product is positive; if they are of opposite signs, the product is negative; and if either is zero, the product is zero. This concept is fundamental in mathematics and is used in various applications, from basic arithmetic to algebraic equations.