Explain and provide an illustrative example of factoring a trinomial.

Answer 1

surely your text has examples and explanations. And remember that google is your friend.

Answer 2

This topic usually requires several days in a standard classroom situation, so it is not possible to answer in a single post of this kind.
I just Googles, "factoring trinomias" and got oodles of websites.
I have been a fan of Khan Academy for years and this one explains a simple quadratic trinomial
https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-quadratic-expressions/v/factoring-quadratic-expressions