How would I factor the trinomial
s^2-11s+30
You know it's going to be
(s-?)(s-?)
You know that the two unknown numbers have to multiply to make 30.
So, there are just a few choices:
1,30 or 2,15 or 3,10 or 5,6
Now, they have to add to 11 to make the middle work out. That makes 5,6 the only choice:
(s-5)(s-6)