If (x - a) is a factor of x³ - ax² + x + 5; the value of a is :

1. $\dfrac{1}{5}$

2. 5

3. -$\dfrac{1}{5}$

4. -5

By factor theorem,

If polynomial ƒ(x) is divided by its factor (x - a) then the remainder ƒ(a) = 0.

Since, x - a is a factor of x³ - ax² + x + 5.

∴ On substituting x = a in x³ - ax² + x + 5, remainder = 0.

∴ a³ - a(a)² + a + 5 = 0

⇒ a³ - a³ + a + 5 = 0

⇒ a + 5 = 0

⇒ a = -5.

Hence, Option 4 is the correct option.