To determine which of the given options is not a polynomial, we first need to understand the definition of a polynomial.
### Step-by-Step Solution:
1. **Definition of a Polynomial**: A polynomial in one variable \( x \) is an expression of the form:
\[
P(x) = A_n x^n + A_{n-1} x^{n-1} + \ldots + A_1 x + A_0
\]
where \( A_n, A_{n-1}, \ldots, A_0 \) are constants (coefficients), \( n \) is a non-negative integer, and \( A_n \neq 0 \).
2. **Identify the Options**: We need to analyze each option to see if it fits the definition of a polynomial.
3. **Option 1**: \( \sqrt{3} x^2 - 2\sqrt{3} x + 5 \)
- This expression contains terms with non-negative integer powers of \( x \) (specifically \( x^2 \) and \( x^1 \)), and the coefficients are constants. Therefore, this is a polynomial.
4. **Option 2**: \( x^3 + 2x^2 - 5x + 4 \)
- This expression also contains terms with non-negative integer powers of \( x \) (specifically \( x^3, x^2, x^1, \) and \( x^0 \)), and the coefficients are constants. Thus, this is a polynomial.
5. **Option 3**: \( 3 + \frac{3}{x} \)
- Here, \( \frac{3}{x} \) can be rewritten as \( 3x^{-1} \). Since the exponent of \( x \) is negative, this does not fit the definition of a polynomial. Therefore, this is not a polynomial.
6. **Option 4**: \( 2x^4 - 3x^2 + 1 \)
- This expression contains terms with non-negative integer powers of \( x \) (specifically \( x^4, x^2, \) and \( x^0 \)), and the coefficients are constants. Thus, this is a polynomial.
7. **Conclusion**: Based on the analysis, the expression that is not a polynomial is:
\[
3 + \frac{3}{x}
\]
### Final Answer:
The option that is not a polynomial is **Option 3: \( 3 + \frac{3}{x} \)**.
