Factor the trinomial, or state that the \( t \) \[ y^{2}-18 y+77 \] Select the correct choice below and, it A. \( y^{2}-18 y+77=\square \) B. The polynomial is prime.

To factor the trinomial \( y^{2}-18y+77 \), we need two numbers that multiply to 77 and add up to -18. The numbers -7 and -11 fit the bill since \( -7 \times -11 = 77 \) and \( -7 + (-11) = -18 \). Therefore, we can write: \[ y^{2}-18y+77 = (y - 7)(y - 11). \] So the correct choice is A. Now you have factored the polynomial successfully, just like a treasure hunt where the clues lead you to the secret vault! Keep an eye out for those pairs of numbers, as they can often lead to fantastic finds in your factoring adventures! If you ever find yourself stuck with trinomials again, don’t forget that using the quadratic formula can be your trusty sidekick too! Just remember, when in doubt, always check to see if the one you're working with can be factored before resorting to the formula. It may surprise you most of the time!