Final answer:
The trinomial x^(2) - 18x + 81 is a perfect square trinomial. It can be factored as (x-9)^2.
Step-by-step explanation:
In mathematics, the process of factoring involves breaking down a mathematical expression into its simplest parts, a critical aspect when simplifying and solving equations. The trinomial given in your question, x^(2) - 18x + 81, is a perfect square trinomial. It can be factored by spotting that it's in the form of (a-b)^2, where a^2 is x^2, -2ab is -18x (with a as x and b as 9) and b^2 is 81 (9 squared). So the factored form is (x-9)^2. Therefore, we have factored the trinomial completely as per the main task.
Learn more about Factoring Trinomials