Use mathematical induction to solve for all positive integers n.
A factor of $\left( n ^ { 3 } + 7 n ^ { 2 } + 6 n \right)$ is:

A)7
B)9
C)8
D)6
E)3

Question

Use mathematical induction to solve for all positive integers n.  
A factor of $\left( n ^ { 3 } + 7 n ^ { 2 } + 6 n \right)$ is:
 
A)7
B)9
C)8
D)6
E)3

Quizplus · Accepted Answer

The expression $ n^3 + 7n^2 + 6n $ can be factored as $ n(n+1)(n+6) $. Since $ n, n+1, $ and $ n+6 $ are three consecutive integers, one of them must be divisible by 3, making the entire product divisible by 3.

Use Mathematical Induction to Solve for All Positive Integers N (n3+7n2+6n)\left( n ^ { 3 } + 7 n ^ { 2 } + 6 n \right)(n3+7n2+6n)

Use Mathematical Induction to Solve for All Positive Integers N $\left( n ^ { 3 } + 7 n ^ { 2 } + 6 n \right)$