Question

Using Remainder Theorem, find the remainder when $$f(x) = 8x^3 - 16x^2 + 14x - 5$$ is divided by $$(2x - 1)$$.

Answer 1

The value that makes $$2x - 1 = 0$$ is $$x = \frac{1}{2}$$.

Therefore, the remainder is $$f\left(\frac{1}{2}\right)$$.

$$f\left(\frac{1}{2}\right) = 8\left(\frac{1}{2}\right)^3 - 16\left(\frac{1}{2}\right)^2 + 14\left(\frac{1}{2}\right) - 5$$

$$= 1 - 4 + 7 - 5$$

$$= -1$$

Hence, the remainder is $$-1$$.