Final answer:
The value of k is 3.5.
Step-by-step explanation:
Given f(x) = 2x² + kr + 15, and the remainder when f(x) is divided by x + 8 is 95, we can use polynomial division to find the remainder. Dividing 2x² + kr + 15 by x + 8, we get a remainder of 95. Setting this equal to the remainder, 95, we can solve for k.
When we divide 2x² + kr + 15 by x + 8, the remainder is given by substituting x = -8 into the polynomial:
2(-8)² + k(-8) + 15 = 95
Simplifying, we have:
128 - 8k + 15 = 95
113 - 8k = 95
Solving for k, we get:
k = 3.5