So the trickiest part about these is finding how to get the middle term. The easiest way to do this is by multiplying your end terms, 3 and -8, and using the factors to find how to get the middle term:
3 x -8 = -24
Factors of 24 = 1,2,3,4,6,8,12,24
Now we need two of these factors to add to make +10, in this case it'd be 2 and 12. The reason this works is because our number is -24, so one of the factors is going to be negative, in this case we make the 2 negative: -2+12=10
Now we set up the equation like so:
3x^2 + 12x -2x - 8
Now simplify by pulling out common terms:
3x(x+4) - 2(x+4)
(3x-2)(x+4)
Ta-da, your polynomial is now 2 binomials
It takes lots of practice, but once you get the hang of it they get easier to do in your head. Keep at it!
