If you put a dime in one hand and a penny in the other hand how do you detemine which hand is holding the penny

  (3D +4)(D -2)

Step-by-step explanation:

The middle term needs to be split into two terms that sum to -2D and have a product of (3d²)(-8) = -24D². You know that -24 has the possible factorizations ...

  -24 = -24·1 = -12·2 = -8·3 = -6·4

This last pair of factors has a sum of -2. So, the middle term of the original expression can be split into the two terms -6D and +4D.

  3D² -2D -8 = 3D² -6D +4D -8

  = 3D(D -2) +4(D -2)

  = (3D +4)(D -2)