Find the greatest common factor of the terms of the \[ 4 n^{3}+8 n^{2} \]

To find the greatest common factor (GCF) of the terms \(4n^3\) and \(8n^2\), we start by identifying the coefficients and the variable parts. The coefficients are 4 and 8. The GCF of 4 and 8 is 4. Next, we look at the variable parts: \(n^3\) and \(n^2\). The GCF of \(n^3\) and \(n^2\) is \(n^2\) since we take the lowest power of \(n\). Combining both results, the GCF of the entire expression \(4n^3 + 8n^2\) is: \[ 4n^2 \] Now, we can factor the original expression using this GCF: \[ 4n^2(n + 2) \] So, the greatest common factor is \(4n^2\).