Using remainder theorem, find the remainder when:

f(x) = 8x² - 2x - 15 is divided by (2x + 3).

By remainder theorem,

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

f(x) = 8x² - 2x - 15

Divisor :

⇒ 2x + 3 = 0

⇒ 2x = -3

⇒ x = -$\dfrac{3}{2}$

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

$\Rightarrow f\Big(-\dfrac{3}{2}\Big) = 8\Big(-\dfrac{3}{2}\Big)^2 - 2\Big(-\dfrac{3}{2}\Big) - 15 \\[1em] = 8\Big(\dfrac{9}{4}\Big) + 2\Big(\dfrac{3}{2}\Big) - 15 \\[1em] = 18 + 3 - 15 \\[1em] = 6.$

Hence, remainder = 6.