A point $(2, n)$ is 5 units away from the point $(-1, 1)$. What is the product of all possible integer values for $n$?
Use the distance formula (squared)
(2 - -1)^2 + ( 1 - n)^2 = 25 simplify
9 + n^2 - 2n + 1 = 25
n^2 - 2n + 10 = 25
n^2 - 2n - 15 = 0 factor
(n - 5) ( n + 3) = 0
Setting each factor to 0and solving for n produces n = 5 and n = -3
Their product = -15
