Question

Which of the following is not a polynomial?

• A. \(\sqrt3x^2-2\sqrt3x+5\)
• B. \(9x^2-4x+\sqrt2\)
• C. \(\frac{3}{2}x^3+6x^2-\frac{1}{\sqrt2}x-8\)
• D. \(x+\frac{3}{x}\)

Answer 1

The Correct Option is D

We are asked to identify which of the following is not a polynomial.
$\sqrt{3}x^2 - 2\sqrt{3}x + 5$ is a polynomial because all the exponents of $x$ are non-negative integers.
$9x^2 - 4x + \sqrt{2}$ is a polynomial because all the exponents of $x$ are non-negative integers.
$\frac{3}{2}x^3 + 6x^2 - \frac{1}{\sqrt{2}}x - 8$ is a polynomial because all the exponents of $x$ are non-negative integers.
$x + \frac{3}{x}$ is not a polynomial because it contains a negative exponent of $x$ ($x^{-1}$).
Thus, the expression $x + \frac{3}{x}$ is not a polynomial.

The correct option is (D): \(x+\frac{3}{x}\)