I have the following matrix:

$\displaystyle \begin{bmatrix}0 & 0 & c\\ 1 & 0 & b\\ 0 & 1 & a\end{bmatrix}$

its characteristic polynomial is $\displaystyle f(x)=x^3-ax^2-bx-c$

I need to prove that this is also its minimal polynomial.

How do I approach this problem?

I can't even factorize this polynomial.