1: factor out 8x and then you have a quadratic left you can solve using the quadratic formula (when you know the zeros of your polynomial you know the factors)
2,3,4: directly apply quadratic formula
5: Let and you have a quadratic through which you can directly solve with the quadratic formula.
6: factor out 3b and then you have a quadratic left.
7: factor 3xy
For finding gcf it's mainly practice but in general if you have a polynomial, say factor out where and