Factoring Trinomials & GCF

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 $x = a^2$ 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 $x^n*y^m + x^t*y^v$ factor out $x^a*y^b$ where $a = min (n,t)$ and $b = min(m,v)$