To determine whether the unknown bacterium is a chemotroph, the best method would be:
growing the bacterium in an agar tube filled with protein to see if it breaks the organic molecules down
Chemotrophs obtain their energy from chemical compounds, often organic molecules, and testing if the bacterium can metabolize the protein would help ascertain if it uses chemical energy. The other options pertain to other metabolic processes such as phototrophy (light to chemical energy), autotrophy (carbon fixing), or specific inorganic compound breakdown.