Question

Using Remainder Theorem, find the remainder when $$f(x) = 9x^2 - 6x + 2$$ is divided by $$(3x - 2)$$.

Answer 1

The value that makes $$3x - 2 = 0$$ is $$x = \frac{2}{3}$$.

Therefore, the remainder is $$f\left(\frac{2}{3}\right)$$.

$$f\left(\frac{2}{3}\right) = 9\left(\frac{2}{3}\right)^2 - 6\left(\frac{2}{3}\right) + 2$$

$$= 4 - 4 + 2$$

$$= 2$$

Hence, the remainder is $$2$$.