How integral values of $k$ exists such that all roots of the polynomial:
$$f(x)=x^3-(k-3)x^2-11x+(4k-8)$$ are also integers.
Could someone please provide me some direction to proceed in this. First I thought first root would be obtained by hit and trial but it is not the case here. I also tried rewriting $x^3-(k-3)x^2-11x+(4k-8)=0$ as $x^3+3x^2-11x-8=k(x^2-4)$ and solve the question graphically but didn't succeed in that. Please give some direction