How is the pattern for a perfect square trinomial used to factor the trinomial?

Step-by-step explanation:

We're going to try two things here.

First an example

x^2 + 10x + 25

If you divide the linear factor by 2 and square the result, you get the last number (25)

The pattern of a trinomial is

x^2 + 2b x + b^2

The factors are

(x + b) (x + b)

Just divide the linear term by 2