Question

if the product of 6 intergers is negative how many of these intergers must be negative

Answer 1

at least 1 must be negative

if remember, 2 negatives multiplied together cancel

if we had 0 negatives, we would get positive
if we had 1 negative, we would get negative
if we had 2 negatives, we would get positive
if we had 3 negative, we would get negative
if we had 4 negatives, we would get positive
if we had 5 negative, we would get negative
if we had 6 negatives, we would get positive


so 1 or 3 or 5 must be negaitve

Answer 2

Only 1 has to be a negative.

A negative times a positive results in a negative. 
SO 5 positive numbers multiplied by a negative integer will indeed ensue in a negative product