2020 · Q1
x³ + x² + 16 is exactly divisible by x, where x is a positive integer. The number of all such possible values of x is
Elementary MathematicsNumber System
- A3
- B4
- C5
- D6
Explanation
For x to divide x^3+x^2+16, x must divide the remainder after removing the x^3+x^2 part, i.e. x must divide 16. The positive divisors of 16 are 1, 2, 4, 8 and 16 - five values in all. Hence the number of such x is 5, option (C).