Explanation

Given 2 is a zero of the polynomial 2x⁴ + x³ + kx² - 8, we substitute x = 2 into the polynomial and set it equal to 0:

2(2)⁴ + (2)³ + k(2)² - 8 = 0

2(16) + 8 + 4k - 8 = 0

32 + 8 + 4k - 8 = 0

32 + 4k = 0

Now, solve for k:

4k = -32

k = -32/4

k = -8