Show that 3x + 2 is a factor of 3x² - x - 2.

3x + 2 = 0 ⇒ x = $-\dfrac{2}{3}$

∴ When given polynomial 3x² - x - 2 is divided by x - 2, the remainder

$= 3\Big(-\dfrac{2}{3}\Big)^2 - \Big(-\dfrac{2}{3}\Big) - 2 \\[1em] = 3 \times \dfrac{4}{9} + \dfrac{2}{3} - 2 \\[1em] = \dfrac{4}{3} + \dfrac{2}{3} - 2 \\[1em] = \dfrac{6}{3} - 2 \\[1em] = 2 - 2 = 0.$

Hence, by factor theorem 3x + 2 is a factor of 3x² - x - 2.