To find the value of k in the given polynomial, we need to use the fact that -2 is a zero of both √2(x p) and x^2 - kx + 2√2.

1. Understanding Zero of a Polynomial:
A zero of a polynomial is a value for which the polynomial evaluates to zero. In other words, if we substitute the zero value into the polynomial, the result will be zero.

2. Zero of √2(x p):
Let's first consider the polynomial √2(x p) where -2 is a zero.
√2(x p) = 0
Since -2 is a zero, we can substitute it into the polynomial:
√2(-2 p) = 0
Simplifying this equation, we get:
-2√2 p = 0
Dividing both sides by -2√2, we find:
p = 0

3. Zero of x^2 - kx + 2√2:
Now, let's consider the polynomial x^2 - kx + 2√2 where -2 is a zero.
x^2 - kx + 2√2 = 0
Substituting -2 into the polynomial:
(-2)^2 - k(-2) + 2√2 = 0
Simplifying this equation, we get:
4 + 2k + 2√2 = 0

4. Solving for k:
We have the equation: 4 + 2k + 2√2 = 0
We can isolate k by moving the other terms to the other side of the equation:
2k = -4 - 2√2
Dividing both sides by 2, we find:
k = (-4 - 2√2) / 2
Simplifying further:
k = -2 - √2

Therefore, the value of k is -2 - √2.

Explanation:
The given problem involves finding the value of k in a polynomial when -2 is a zero for both √2(x p) and x^2 - kx + 2√2.
We first determine the value of p by substituting -2 into √2(x p) and solving for p. This gives us p = 0.
Then, we substitute -2 into x^2 - kx + 2√2 and solve for k. This leads us to k = -2 - √2.
So, the value of k is -2 - √2.