#### Answer

(x-5)(x-9)

#### Work Step by Step

$x^{2}$ - 14x + 45
step 1. Enter x as the first term of each factor
$x^{2}$ - 14x + 45 = (x__)(x _)
Step 2. To find the second term of each factor, we must find two integers whose product is 45 and whose sum is -14
List pairs of factors of the constant, 45
(1,45)(-1,-45)(-3,-15)(3,15)(-5,-9)(5,9)
step 3. The correct factorization of $x^{2}$ - 14x + 45 is the one in which the sum of the Outside and Inside products is equal to -14x.
So (-5,-9) satisfy the condition
$x^{2}$ -14x + 45 = $x^{2}$ -5x -9x + 45 = (x-5)(x-9)