What is the product of the two integer values for $x$ for which $|x^2 - 16|$ is a prime number?

-9

Step-by-step explanation:

x² - 16 = (x - 4) (x + 4)

This magnitude of this product can only be prime if one of the factors is ±1. Any other integer value of x will produce a composite number (or zero).

... For x-4 = ±1, x = 3 or 5

... For x+4 = ±1, x = - 3 or - 5

The values of x that are ±3 both give |x²-16| = 7, a prime.

The values of x that are ±5 both give |x²-16| = 9, not a prime.

The two values of x that are of interest are x=-3 and x=3. Their product is ...

... (-3) · (3) = - 9