Using remainder theorem, find the remainder when:

f(x) = 8x³ - 16x² + 14x - 5 is divided by (2x - 1).

By remainder theorem,

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

Let f(x) = 8x³ - 16x² + 14x - 5

Divisor :

⇒ (2x - 1) = 0

⇒ 2x = 1

⇒ x = $\dfrac{1}{2}$

Substituting x = $\dfrac{1}{2}$ in f(x), we get :

$\Rightarrow f\Big(\dfrac{1}{2}\Big) = 8\Big(\dfrac{1}{2}\Big)^3 - 16\Big(\dfrac{1}{2}\Big)^2 + 14\Big(\dfrac{1}{2}\Big) - 5 \\[1em] = 8\Big(\dfrac{1}{8}\Big) - 16\Big(\dfrac{1}{4}\Big) + 14\Big(\dfrac{1}{2}\Big) - 5 \\[1em] = 1 - 4 + 7 - 5 \\[1em] = -1.$

Hence, remainder = -1.