# How do you factor by grouping 3n^2 - 8n + 4?

May 17, 2015

$3 {n}^{2} - 8 n + 4$

$= 3 {n}^{2} - 2 n - 6 n + 4$

$= \left(3 {n}^{2} - 2 n\right) - \left(6 n - 4\right)$

$= n \left(3 n - 2\right) - 2 \left(3 n - 2\right)$

$= \left(n - 2\right) \left(3 n - 2\right)$

The 'trick' was to split the original $- 8 n$ term into two parts such that the resulting ratio of the first and second terms $3 {n}^{2}$ and $- 2 n$ was the same as the ratio of the third and fourth terms $- 6 n$ and $4$.