I am trying to manually calculate the discrete time form of a continuous time system using the zero order hold method.

The continuous time transfer function is:

g(s) = 4
s^2 + 4.8s + 2

The sampling time I would like to consider is Ts= 0.01

The equation I believe that I need to use is:
g(z) =
z - 1 Z[g(s)/s]

I had attempted to derive partial fractions and solve that way but was unable to factorise the denominator.

According to Matlab the final answer should be:

g(z) = 0.0001968z + 0.0001937
z^2 - 1.953z + 0.9531

Any help would be much appreciated!