Question

what will be the sign of the product if multiple together 15 negative integers and 4 positive integer

Answer 1

the sign will be negative
-+-=+
+++=+
so the last negative number will make the number negative

Answer 2

the product of an even number of negative integers is positive.
the product of an odd number of negative integers is negative.
the product any number of even or odd positive integers gives positive integer as the product.

so the product of 15 negative will be negative as there are odd number of numbers.
And the product of 4 positive numbers is positive.

So finally we get negative * positive whose product is negative.

So the final answer is negative.