Final answer:
The environmental factor needed to support life on another planet is liquid water, as it's essential for sustaining life and biochemical processes. In the case of finding an exoplanet with signs of life-supporting elements, further investigation would be warranted, with substantial resources dedicated to such efforts.
Step-by-step explanation:
One of the environmental factors that is needed to support life on another planet is liquid water. Liquid water acts as a solvent, which is essential for the formation and interactions of biomolecules necessary for life. Since all known life on Earth requires liquid water, the guiding principle adopted by scientists in the search for extra-terrestrial life has been to "follow the water." This search involves identifying environments within the right range of temperatures and pressures where water can exist in a liquid state. On Earth, water is part of the hydrosphere which includes fresh water in rivers and lakes, saltwater of oceans and estuaries, as well as groundwater and water vapor.
When considering an exoplanet that exhibits signs of oxygen and methane in its atmosphere, astronomers should pursue further investigation given the potential for life. This could involve allocating significant resources for the development of technology capable of gathering more detailed information, possibly through space missions or advanced telescopes. The effort and funds invested would be significant, but the potential discovery of life-supporting conditions or actual life on another planet justifies such an investment.