What is the factored form of 6n4 – 24n3 18n?

1) Extract common factor 6n

6n^4-24n^3+18n=6n[n^3-4n^2+3]

2) For more clearity I will work separatedly the expression that is inside square brackets:

n^3-4n^2+3 = n^3 - n^2  -3n^2 +3 =(n^3 -n^2) - (3n^2 - 3) = n^2 ( n-1) - 3(n^2 -1) =

= n^2(n-1) -3(n-1)(n+1) = (n-1)[n^2 -3(n+1)] =(n-1)[n^2 -3n -3]

3) no i will put all the factors together

6n(n-1)(n^2-3n-3)