let n be any integer.
what, if anything, can be said about the sign of the following expression?
-n^2-4
The sign of the expression -n^2-4 depends on the value of n.
If n is a positive integer, then -n^2 will be negative because a positive number squared is positive and then negating it makes it negative. So, -n^2-4 will be negative since subtracting 4 from a negative number will still result in a negative number.
If n is a negative integer, then -n^2 will be positive because a negative number squared is positive. So, -n^2-4 will be negative since subtracting 4 from a positive number will result in a negative number.
If n is zero, then -n^2 will be zero because any number multiplied by zero is zero. So, -n^2-4 will be -4.
In summary, the sign of the expression -n^2-4 can be negative, zero, or positive depending on the value of n.