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

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

Step-by-step 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).

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