Question

What factors primarily determine a particular biome?

Answer 1

see below...

Explanation:

The primary factor which determines a biome is the climate. Temperature and precipitation essentially determines what kind of growing season or soil quality the terrain may have,which therefore affects the growth of plants living there.

Other factors may include: humidity, pollution (such as air, noise...), daylight intensity

Answer 2

Climate is the most important abiotic factor in determining a biome while biomes are defined on the basis of vegetation / plant types.

Explanation:

• Plant types in a biome is directly influenced by abiotic factors which influence photosynthesis, of which few are climatic: such as
  TEMPERATURE and
  PRECIPITATION.
• The above factors together with SOIL type would determine type of vegetation that grows in an area.
• Please note that temperature changes with latitude and altitude, accordingly the vegetation would vary.
• Sunlight hours also vary with latitude and plants are entirely dependent on sunlight for growth and development.
• Likewise precipitation level differs in coastal and inland areas, higher level of precipitation beneficial for plant growth.

You may have an idea of distribution of terrestrial biomes depending on latitude, from the following illustration

Also read this answer on related topic.