Which of the following is not a polynomial? [1]a) √3x2 − 2√3x + 5 b) x + 3c) 9x2 − 4x + √2 d) 3 x3 + 6x2 − 1 x − 8

To determine which of the given options is not a polynomial, we need to review the definition of a polynomial. A polynomial is an expression that comprises variables raised to whole number powers and coefficients that are real numbers. Expressions that include square roots, negative exponents, or variables in the denominator are not considered polynomials.

Step 1: Analyze Each Option

1. Option a: $\sqrt{3}x^2 - 2\sqrt{3}x + 5$

   • Contains square roots. Not a polynomial.

2. Option b: $x + 3$

   • Both terms are non-negative integers' powers. This is a polynomial.

3. Option c: $9x^2 - 4x + \sqrt{2}$

   • Contains square roots. Not a polynomial.

4. Option d: $3x^3 + 6x^2 - 1x - 8$

   • All terms consist of whole number powers of $x$. This is a polynomial.

Step 2: Conclusion

Among the options provided, both option (a) and option (c) contain square root terms, making them not polynomials. However, since the question asks for one specific answer that is not a polynomial, the first option mentioned is typically sufficient.

Final Answer

The option that is not a polynomial is: a) $\sqrt{3}x^2 - 2\sqrt{3}x + 5$.