Explanation

To find the value of k, use the Factor Theorem:

If a polynomial f(x) is completely divisible by (x - a), then f(a) = 0.

In this case, the polynomial is:

f(x) = 3x³ + 9x² - (3k - 4)x + 2

Since it's divisible by (x - 1), substitute x = 1:

f(1) = 3(1)³ + 9(1)² - (3k - 4)(1) + 2

= 3 + 9 - 3k + 4 + 2

= 18 - 3k

Set f(1) = 0:

18 - 3k = 0

Solve for k:

3k = 18

k = 6