Factor by grouping each of the following.

3x² - 2x + 12x - 8

Solution

          3x² - 2x + 12x - 8

In this case we collect the first two terms & the final two terms as illustrated here,

                          (3x²  - 2x ) + (12 x - 8)

Notice that we can factor an x out of the first grouping & a 4 out of the second grouping. Doing this gives,

3x² - 2x + 12x - 8=x (3x - 2) + 4 (3x - 2)

Now we can see that we can factor out a common factor of 3x - 2 thus let's do that to the final factored form.

3x² - 2x + 12x - 8 = (3x - 2) ( x + 4)

And we're done. That's all that there is to factoring through grouping.  Note down again that it will not always work & sometimes the single way to know if it will work or not is to attempt it and see what you get.