#### Answer

prime

#### Work Step by Step

$x^{2}$ -9x +81
step 1. Enter x as the first term of each factor
$x^{2}$ -9x +81= (x__)(x _)
Step 2. To find the second term of each factor, we must find two integers whose product is 81 and whose sum is -9
List pairs of factors of the constant, 81
(1,81)(-1,-18)(3,27)(-3,-27))(9,9)(-9,-9)
step 3. The correct factorization of $x^{2}$ -9x +81 is the one in which the sum of the Outside and Inside products is equal to -9x.
Since there are no factors that can sum up to -9, this polynomial is prime.