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)