Finding a congruence chain (linear and quadratic) equivalent to a polynomial

Question

I want to find a congruence chain (linear and quadratic) equivalent to $2x^2+3x-k \equiv 0 (\mod5)$, with $k \in \mathbb{Z}$. I've started with considering the polynomial for $x=1,2,3,4$ but I don't know how one can find a congruence chain.

Can someone explain me what it means?

Thanks