Question

pls help me solving this question​

Answer 1

Answer:

It's easy, but one has to just think about it.

Step-by-step explanation:

x³ +x²+16 is exactly divisible by x.

(Don't tell anyone, I'm now going to divide the polynomial by x)

${x}^{2} + x + \frac{16}{x}$

is an integer.

(whatever the value of x is, we are interested in 16/x).

$\frac{16}{x} is \: \: an \: integer.$

(which means that 16 should be divisible by x).

Which Implies that all the possible values of x are:-

1, 2, 4, 8 and 16. (Negative versions also should be counted, but as in the question, x is a positive integer)

Therefore, the exact answer is 5.