Question

Using Remainder Theorem, find the remainder when $$f(x) = 8x^2 - 2x - 15$$ is divided by $$(2x + 3)$$.

Answer 1

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

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

$$f\left(-\frac{3}{2}\right) = 8\left(-\frac{3}{2}\right)^2 - 2\left(-\frac{3}{2}\right) - 15$$

$$= 18 + 3 - 15$$

$$= 6$$

Hence, the remainder is $$6$$.