No, always positive.
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-- If the two integers have the same sign, their quotient is positive. -- If the two integers have different signs, their quotient is negative.
If both integers are positive or both negative then the quotient is positive. If they are one of each then the quotient is negative.
Their quotient is positive if the integers have the same sign;negative if the integers have different signs;zero if the dividend is zero (and the divisor is not).
Yes, it is.
That is false. The product of two negative integers is always positive.