Answer:
6n(n - 1)(n^2 - 3n - 3).
Explanation:
The GCF = 6n.
6n^4 - 24n^3 + 18n
= 6n(n^3 - 4n^2 + 3)
Putting n = 1 in the expression in the parentheses:
(1)^3 - 4(1)^2 + 3 = 0 so n - 1 is a factor.
Dividing:
n - 1 ) n^3 - 4n^2 + 0n + 3 ( n^2 - 3n - 3
n^3 - n^2
-3n^2 + 0n
-3n62 + 3n
- 3n + 3
-3n + 3
So the factors are 6n(n - 1)(n^2 - 3n - 3).