Deducing a coefficient from a cubic polynomial? I fully answered the question, and got that $k=-3$, but the answer says it's positive. Can anyone show me my mistake?
"Given that $x-2$ is a factor of the polynomial $x^3 - kx^2 - 24x + 28$, find $k$ and the roots of this polynomial."
Using factor theorem, I realised that $P(2)$ is equivalent to $0$, therefore $2^3 - 2^2k - 24(2) + 28 = 0$
I solved it algebraically and got that $k=-3$, but the answers say it was $k=3$. Did I make a simple error?
Any help would be appreciated. 

No error on your part:
If you've copied the problem correctly, then your solution is correct: $k = -3$.
I was very careful in calculating, as I'm sure you were, in double checking, so if $(x - 2)$ is a factor for your given polynomial, then $k$ must be $-3$. 
Typo/misprint I suspect, in your text: a typo in the solution, or a misprint of the desired polynomial. 
E.g. If the polynomial had been 
$$x^3 \color{blue}{\large \bf +} 4k^2 - 24x + 28\quad \text{and}\;\; (x-2) \;\text{is a factor}$$
then $k = 3$. 
