For the question " If $f(x)$ is a polynomial with constant term $10$ having a factor $(x-k)$ where $k$ is an integer, then find the possible value of $k$", the options given are $-20, 20, 8$ and $5$.
I get that by remainder theorem, $k$ should divide $f(x)$, so, $f(k)$ would be zero.
Since $f(x)$ is not given, I assumed that to be $[x/2 + 10]$ to satisfy the first option. Same way, other polynomials can also be imagined and all options would satisfy. But the answer is given as only $5$.
If they had asked least positive value of $k$ then I may have understood but that is not the case. They have clearly asked 'possible value of $k$', so all the options should be correct.
But as is usually the case, I miss some fine detail, so, need your help yo figure that out. Thanks.