Question 1130807
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We only need to count the number of negative factors in a whole expression (numerator and denominator) to determine whether the expression value is positive or negative.  An even number of negative factors makes the expression value positive; an odd number makes the expression value negative.<br>
The total number of factors in the given expression is 12; and it is given that the value of that expression is positive.<br>
In every one of the given answer choices, there is an even number of factors of w; so the product of the factors of w is positive in every answer choice.  That means the sign of the expression is always determined by the number of factors of u and v.<br>
The sum of the numbers of factors of u and v in the given expression is 8, an even number.  That means any other expression in which the sum of the factors of u and v is even will have the same sign as the given expression.<br>
The sum of the numbers of factors of u and v in all the answer choices except B is even, so all of those answer choices must be positive.<br>
ANSWER: The only answer choice that does not have to be positive is B.