Question

On dividing $$(ax^3 + 9x^2 + 4x - 10)$$ by $$(x + 3)$$, we get 5 as remainder. Find the value of $$a$$.

Answer 1

Let $$f(x) = ax^3 + 9x^2 + 4x - 10$$.

Since the divisor is $$x + 3$$, the remainder is $$f(-3)$$.

$$f(-3) = a(-3)^3 + 9(-3)^2 + 4(-3) - 10$$

$$= -27a + 59$$

The remainder is $$5$$, so

$$-27a + 59 = 5$$

$$\Rightarrow -27a = -54$$

$$\Rightarrow a = 2$$