Find the value of 'a' if x - a is a factor of the polynomial 3x 3 + x 2 - ax - 81.

By factor theorem,

If x - a is a factor of f(x), then f(a) = 0.

Given,

x - a is a factor of the polynomial 3x³ + x² - ax - 81.

⇒ x - a = 0

⇒ x = a.

∴ 3a³ + a² - a.a - 81 = 0

⇒ 3a³ + a² - a² - 81 = 0

⇒ 3a³ - 81 = 0

⇒ 3a³ = 81

⇒ a³ = $\frac{81}{3}$

⇒ a³ = 27

⇒ a³ = 3³

⇒ a = 3.

Hence, value of a = 3.