The product of two integers can be positive, negative, or zero depending on the values of those integers.
1. **Positive Product**: If both integers are positive (e.g., 3 and 5), their product will also be positive (3 × 5 = 15). Similarly, if both integers are negative (e.g., -3 and -5), the product will also be positive (-3 × -5 = 15). This is because the multiplication of two like signs results in a positive sign.
2. **Negative Product**: If one integer is positive and the other is negative (e.g., 3 and -5), the product will be negative (3 × -5 = -15). This occurs because the multiplication of unlike signs results in a negative sign.
3. **Zero Product**: If either of the integers is zero (e.g., 0 and 5), the product will be zero (0 × 5 = 0). In any multiplication, if at least one factor is zero, the result will always be zero.
In summary: the product of two integers will be positive when both are of the same sign (either positive or negative), negative when they have different signs, and zero if at least one of the integers is zero.