Answer
$(x - 9)^2$
Work Step by Step
To factor a quadratic polynomial in the form $x^2 + bx + c$, we look at factors of $c$ such that, when added together, equal $b$.
For the polynomial $x^2 - 18x + 81$, $c=81$, so look for the factors of $81$ that when added together will equal $-18$. This means that we need two negative factors because two negative numbers multiplied together yield a positive number, but when added together will yield a negative number. Here are the possibilities:
$81=(-81)(-1)$
$-81+(-1) = -82$
$81=(-9)(-9)$
$-9+(-9) = -18$
The second pair, $-9$ and $-9$is the one we are after.
Thus, the factored form of the trinomial is:
$$(x - 9)(x - 9)$$
The expression above can be written as :
$$(x - 9)^2$$
