Question

x³ + x² + 16 is exactly divisible by x, where x is a positive integer. The number of all such possible values of x is 
1. 3
2. 4
3. 5
4. 6

Answer 1

Correct Answer - Option 3 : 5

Given :

x3 + x2 + 16 is exactly divisible by x, where x is a positive integer

Calculations :

Let a number N be equal to x3 + x2 + 16. 

N = x3 + x2 + 16 

Now divide N/x 

N/x = (x3 + x2 + 16)/x 

⇒ x² + x + (16/x)

As N is divisible by x so 16 must be divisible by x 

Values of x that can divide 16 are 1, 2, 4, 8 and 16 

So there are total 5 values of x that can divide N without leaving the remainder.

∴ Option 3 is the correct answer.