Question

Suppose 3s represents an even integer. What polynomial represents the product of 3s, the even integer that comes just before 3s, and the even integer that comes just after 3s?

Answer 1

3s = 2k for some integer k

The even integer before 2k is 2k - 2

The even integer after 2k is 2k+2


So the product of the three is


2k(2k-2)(2k+2)

2k(4k^2 - 4)

8k^2 - 8