<u><em>Answer:</em></u>
K = -47.5
<u><em>Explanation:</em></u>
The zero of an equation is a number that when substituted in the equation gives the result zero
<u>We are given that:</u>
4 is a zero of f(x) = 3x³ + kx - 2
<u>This means that:</u>
When we substitute x = 4 in f(x) the result will be zero
<u>Therefore:</u>
3(4)³ + k(4) - 2 = 0
<u>Now, we simply solve for K as follows:</u>
3(4)³ + k(4) - 2 = 0
3(64) + 4k - 2 = 0
192 + 4k - 2 = 0
190 + 4k = 0
4k = -190
k = -47.5
Hope this helps :)