Using remainder theorem, find the remainder when:

f(x) = 9x² - 6x + 2 is divided by (3x - 2).

By remainder theorem,

If f(x) is divided by (x - a), then remainder = f(a).

f(x) = 9x² - 6x + 2

Divisor :

⇒ (3x - 2) = 0

⇒ 3x = 2

⇒ x = $\dfrac{2}{3}$

Substituting x = $\dfrac{2}{3}$ in f(x), we get :

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

Hence, remainder = 2.