Factor by grouping each of the following.
3x^{2} - 2x + 12x - 8
Solution
In this case we collect the first two terms & the final two terms as illustrated here,
(3x^{2} - 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,
3x^{2} - 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.
3x^{2} - 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.