CTK Exchange . Should anything be unclear you promise to point this out to me. Before I start let me remark on your terminology. You mention binomials and trinomials.
Binomials have two terms and are linear.
You do not generally factor a binomial. I personally prefer the notion of degree and seldom refer to polynomials as bi- or trinomials. One major point to understand. In other words, two problems Find all roots of a given polynomial P Factor a given polynomial P are absolutely equivalent. I would guess you have not yet studied complex numbers.