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The sign of the product of four integers depends on the signs of the individual integers. There are 4 cases:

1) When all 4 integers share the same sign and all are non-zero (either all are positive or all are negative), the product is positive.

2) When 3 of the 4 integers share the same sign and all are non-zero (3 are positive and 1 is negative; or 3 are negative and 1 is positive), the product is negative.

3) When 2 of the integers are positive non-zero and the other 2 of the integers are negative non-zero, the product is positive.

4) If even one of the integers is zero, the product is zero (no sign - it is neither positive nor negative).

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