Question

Which of the following is not a polynomial

• A. \( \sqrt{3}x^2 - 5\sqrt{2}x + 3 \)
• B. \( 3x^2 - 4x + \sqrt{5} \)
• C. \( x + 2\sqrt{x} \)
• D. \( \frac{1}{5}x^3 - 3x^2 + 2 \)

Hint:

A polynomial cannot have fractional or negative exponents.

Answer 1

The Correct Option is C

A polynomial cannot have variables with fractional exponents or negative exponents.
- \( \sqrt{3}x^2 - 5\sqrt{2}x + 3 \) is a polynomial (constant coefficients).
- \( 3x^2 - 4x + \sqrt{5} \) is a polynomial.
- \( x + 2\sqrt{x} \) is not a polynomial as \( \sqrt{x} = x^{1/2} \).
- \( \frac{1}{5}x^3 - 3x^2 + 2 \) is a polynomial.
Thus, the non-polynomial is \( x + 2\sqrt{x} \).