Explanation:
Azotobacter and Bacillus polymyxa are examples of non-symbiotic nitrogen-fixing bacteria. Here's a detailed explanation of why they fall into this category:

Non-symbiotic Nitrogen-fixers:
Non-symbiotic nitrogen-fixing bacteria are those bacteria that can fix atmospheric nitrogen (N2) into a form that can be utilized by plants. These bacteria do not require a symbiotic relationship with plants to carry out nitrogen fixation. They are free-living bacteria found in soil, water, and other environments.

Azotobacter:
Azotobacter is a genus of bacteria that is known for its ability to fix atmospheric nitrogen. It is found in soil, water, and the rhizosphere of plants. Azotobacter can convert atmospheric nitrogen into ammonia, which can be used by plants as a nutrient. It is considered a non-symbiotic nitrogen-fixing bacterium because it does not form a mutualistic relationship with plants.

Bacillus polymyxa:
Bacillus polymyxa is another example of non-symbiotic nitrogen-fixing bacteria. It is a Gram-positive bacterium that can fix atmospheric nitrogen. It is found in soil and has the ability to produce a variety of antimicrobial compounds. Bacillus polymyxa can form endospores, which help it survive under harsh environmental conditions.

Distinguishing Factors:
There are a few factors that distinguish non-symbiotic nitrogen-fixing bacteria from other types:

1. Independence: Non-symbiotic nitrogen-fixing bacteria can fix nitrogen without the need for a symbiotic relationship with plants or other organisms.

2. Free-living: They are free-living bacteria that can be found in various environments such as soil, water, and the rhizosphere of plants.

3. Ammonia Production: These bacteria have the ability to convert atmospheric nitrogen into ammonia, which can be used by plants as a nutrient.

4. No Disease-causing: Unlike disease-causing bacteria, non-symbiotic nitrogen-fixing bacteria do not cause harm to plants or animals.

Therefore, Azotobacter and Bacillus polymyxa are examples of non-symbiotic nitrogen-fixing bacteria because they can fix atmospheric nitrogen into a usable form without forming a symbiotic relationship with plants.