Question

When is the product of two nonzero integers less than or equal to both of the two factors?

Answer 1

The correct answer is:

When one of the factors is negative and one is positive.

Step-by-step explanation:

Multiplying two positive numbers would result in a positive answer that is larger than both of the factors.

Multiplying two negative numbers would result in a positive answer; this would by definition be larger than both of the factors.

Multiplying a positive by a negative number results in a negative number, and it would be a negative number that is farther away from zero than the negative factor. Since the product is negative, it is smaller than the positive factor; since it is farther from zero than the negative factor, it is smaller than the negative factor.

Answer 2

If the factors are both non-zero integers, then

-- Their product is less than either factor when one and only one of them
is negative.

-- Their product is equal to one of the factors when they're both positive
and one of them is ' 1 '.