the sum of three consecutive even integers is the same as their product. What is the least of these three integer?

Question

A question from math book

Answer 1

n-2, n, and n+2 are the integers

n-2+n+n+2=(n-2)(n)(n+2)

3n=n(n^2-4)

3n=n^3-4n

n^3-4n-3n=0

n^3-7n=0

n(n^2-7)=0

n^2-7=0 will not yield an integer

n=0

n-2=0-2=-2

n+2=0+2=2

the integers are -2, 0, and 2

the sum is 0 and the product is zero because of the 0 as one of the factors