If (3x - 2) is a factor of 3x³ - kx² + 21x - 10, find the value of k.

f(x) = 3x³ - kx² + 21x - 10

If, (3x - 2) or $3(x - \big(\dfrac{2}{3}\big))$ is a factor of f(x) then f($\dfrac{2}{3}$) = 0

$\therefore 3\big(\dfrac{2}{3}\big)^3 - k\big(\dfrac{2}{3}\big)^2 + 21\big(\dfrac{2}{3}\big) - 10 = 0 \\[1em] \Rightarrow 3\big(\dfrac{8}{27}\big) - k\big(\dfrac{4}{9}\big) + 14 - 10 = 0 \\[1em] \Rightarrow \dfrac{8}{9} - \dfrac{4k}{9} + 4 = 0 \\[1em] \Rightarrow \dfrac{8 - 4k + 36}{9} = 0 \\[1em] \Rightarrow 44 - 4k = 0 \\[1em] \Rightarrow 4k = 44 \\[1em] k = 11.$

Hence, the value of k is 11.