Answer
(x-3)(x-5)
Work Step by Step
$x^{2}$ - 8x + 15
step 1. Enter x as the first term of each factor
$x^{2}$ - 8x + 15 = (x__)(x _)
Step 2. To find the second term of each factor, we must find two integers whose product is 15 and whose sum is -8
List pairs of factors of the constant, 15
(1,15)(-1,-15)(-3,-5)(3,5)
step 3. The correct factorization of $x^{2}$ - 8x + 15 is the one in which the sum of the Outside and Inside products is equal to -8x.
So (-3,-5) satisfy the condition
$x^{2}$ -8x + 15 = $x^{2}$ -3x -5x + 15 = (x-3)(x-5)
