Final answer:
To factor the trinomial x²-22x+121, we recognize it as a perfect square and determine that the factors are (x-11)(x-11), which simplifies to (x-11)².
Step-by-step explanation:
To factor the trinomial x²-22x+121 completely, we are looking for two binomials that multiply to give the original trinomial. In this case, we notice that the trinomial is a perfect square because 121 is the square of 11, and the middle term, -22x, is twice the product of 11 and x. Therefore, the factors of the trinomial are (x-11)(x-11), which can be written as (x-11)².
To verify, we can expand the binomials: (x-11)(x-11) = x² - 11x - 11x + 121 = x² - 22x + 121, which is the original trinomial. Hence, we have factored the trinomial correctly.