Problem
ALG-B1-M09-P011 Three consecutive integers
#11
★★★☆☆ Level 3 of 5
Prove that \(n^3+3n^2+2n\) is divisible by \(6\) for every integer \(n\).
Factor the expression.
\(n^3+3n^2+2n=n(n+1)(n+2)\). This is the product of three consecutive integers, so it is divisible by \(6\).
The same idea, but the expression must first be recognized.