On dividing (ax³ + 9x² + 4x - 10) by (x + 3), we get 5 as remainder. Find the value of a.

By remainder theorem,

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

Let f(x) = ax³ + 9x² + 4x - 10

Given,

Remainder = 5

Divisor :

⇒ x + 3 = 0

⇒ x = -3.

Substituting x = -3 in f(x), will give remainder 5.

⇒ f(-3) = 5

⇒ a(-3)³ + 9(-3)² + 4(-3) - 10 = 5

⇒ a(-27) + 81 - 12 - 10 = 5

⇒ -27a + 81 - 22 = 5

⇒ -27a + 59 = 5

⇒ -27a = 5 - 59

⇒ -27a = -54

⇒ a = $\dfrac{-54}{-27}$

⇒ a = 2.

Hence, the value of a = 2.