Question

factor by using gcf: 8n³ + 2n² 2n²(4n - 1) n²(8n + 2) 2n²(4n + 1) 3n(4n + 1)

Explanation:

Step1: Find GCF of coefficients and variables

For coefficients 8 and 2, GCF is 2. For variables \(n^3\) and \(n^2\), GCF is \(n^2\). So overall GCF is \(2n^2\).

Step2: Divide each term by GCF

Divide \(8n^3\) by \(2n^2\): \(\frac{8n^3}{2n^2}=4n\). Divide \(2n^2\) by \(2n^2\): \(\frac{2n^2}{2n^2}=1\).

Step3: Factor out GCF

Factor out \(2n^2\) from \(8n^3 + 2n^2\), we get \(2n^2(4n + 1)\).

Answer:

C. \(2n^2(4n + 1)\) (assuming the orange option is labeled as C, if the options are labeled A, B, C, D with A being green, B purple, C orange, D teal)