Short Answer 
The evaluation of the polynomials reveals that Options 1, 4, and 5 are confirmed as prime polynomials, meaning they cannot be factored into lower-degree polynomials. In contrast, Options 2 and 3 can be factored, thus they are not prime.
Step 1: Identify Prime Polynomials
To determine whether a polynomial is a prime polynomial, you must first understand that it cannot be factored into products of lower-degree polynomials. The prime polynomials identified in the original text are represented by options 1, 4, and 5. Each polynomial must be thoroughly assessed to ensure it meets this criterion.
Step 2: Evaluate Each Option
It’s essential to evaluate each polynomial option to see if they can be factored. The evaluation should be done in the following manner:
- 1. Option 1: (15x^2 + 10x – 9x + 7) – confirmed as a prime polynomial.
- 2. Option 2: (20x^2 – 12x + 30x – 18) – can be factored; thus, it is not prime.
- 3. Option 3: (6x^3 + 14x^2 – 12x – 28) – can be factored; thus, it is not prime.
- 4. Option 4: (8x^3 + 20x^2 + 3x + 12) – confirmed as a prime polynomial.
- 5. Option 5: (11x^4 + 4x^2 – 6x^2 – 16) – confirmed as a prime polynomial.
Step 3: Conclusion on Prime Status
After evaluating the given polynomials, we conclude which are prime based on their factorizability. The findings indicate:
- Prime Polynomials: Options 1, 4, and 5.
- Not Prime Polynomials: Options 2 and 3.
This clear assessment allows us to understand which polynomials satisfy the definition of being prime. Always ensure to show detailed working in practical applications for better understanding.