What is the factored form of 6n^4 - 24n^3 + 18n?

1. Identify the greatest common factor (GCF): Examine the coefficients (6, -24, 18) and the variables ($n^4$, $n^3$, $n$). The GCF of the coefficients is 6. The GCF of the variables is $n$ (the lowest power of $n$ present in all terms). Therefore, the GCF of the entire expression is $6n$.
2. Factor out the GCF: Divide each term of the original expression by the GCF ($6n$).
- For the first term: $\frac{6n^4}{6n} = n^3$
- For the second term: $\frac{-24n^3}{6n} = -4n^2$
- For the third term: $\frac{18n}{6n} = 3$
3. Write the factored expression: The factored form is the GCF multiplied by the sum of the results from step 2. So, the factored form is $6n(n^3 - 4n^2 + 3)$.