Find the value of k, if 3x - 4 is a factor of the expression 3x² + 2x - k.

3x - 4 = 0 ⇒ x = $\dfrac{4}{3}$

Since, 3x - 4 is a factor of 3x² + 2x - k

∴ On substituting x = $\dfrac{4}{3}$ in 3x² + 2x - k, remainder = 0.

$\Rightarrow 3\Big(\dfrac{4}{3}\Big)^2 + 2\Big(\dfrac{4}{3}\Big) - k = 0 \\[1em] \Rightarrow 3 \times \dfrac{16}{9} + \dfrac{8}{3} - k = 0 \\[1em] \Rightarrow \dfrac{16}{3} + \dfrac{8}{3} - k = 0 \\[1em] \Rightarrow \dfrac{16 + 8}{3} = k \\[1em] \Rightarrow k = \dfrac{24}{3} = 8.$

Hence, k = 8.