Question

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

Explanation:

Step1: Find GCF of coefficients

The coefficients are 8 and 2. The greatest common factor of 8 and 2 is 2.

Step2: Find GCF of variables

The variable terms are $n^3$ and $n^2$. The greatest common factor is $n^2$.

Step3: Combine GCFs

The overall GCF is $2n^2$.

Step4: Factor out GCF

Divide each term by $2n^2$:
$\frac{8n^3}{2n^2} = 4n$, $\frac{2n^2}{2n^2} = 1$
So $8n^3 + 2n^2 = 2n^2(4n + 1)$

Answer:

2n²(4n + 1)