## Thinking Mathematically (6th Edition)

$x^{2}$ -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.