#### Answer

prime

#### Work Step by Step

$x^{2}$ - 8x +32
step 1. Enter x as the first term of each factor
$x^{2}$ - 8x +32= (x__)(x _)
Step 2. To find the second term of each factor, we must find two integers whose product is 32 and whose sum is -8
List pairs of factors of the constant, 32
(1,32)(-1,-32)(2,16)(-2,-16)(4,8)(-4,-8)
step 3. The correct factorization of $x^{2}$ - 8x +32 is the one in which the sum of the Outside and Inside products is equal to -8x.
Since there are no factors that can sum up to -8, this polynomial is prime.