Question

Which of the following is not a polynomial?

• A. \( x^2 + \sqrt{5} \)
• B. \( 9x^2 - 4x + \sqrt{2} \)
• C. \( \frac{1}{2} x^3 + \frac{3}{5} x^2 + 8 \)
• D. \( x + \frac{3}{x} \)

Hint:

A polynomial must have: - Whole number exponents. - Finite number of terms.

Answer 1

The Correct Option is D

Step 1: A polynomial must have whole number exponents.
Step 2: Checking options:
- \( x^2 + \sqrt{5} \) is a polynomial (constant term can be an irrational number).
- \( 9x^2 - 4x + \sqrt{2} \) is also a polynomial.
- \( \frac{1}{2} x^3 + \frac{3}{5} x^2 + 8 \) is a polynomial.
- \( x + \frac{3}{x} \) is not a polynomial since \( x^{-1} \) is not a whole number.