Question

Which of the following expressions is a polynomial?

• A. $\sqrt{x}$
• B. $\left(\frac{3}{4}\right)x$
• C. $x^{3/4}$
• D. $x^{-2}$

Answer 1

The correct option is B $\left(\frac{3}{4}\right)x$

The exponent of the polynomial variable should be whole number.
i) $\sqrt{x}$ can be written as $x^{1/2}$ .It is not a polynomial, since the exponent, which is $\frac{1}{2}$, is not a whole number.
ii) $\left(\frac{3}{4}\right)x$ is a polynomial, since the exponent on the variable, which is 1, is a whole number.
iii) $x^{\frac{3}{4}}$ is not a polynomial as the exponent, which is $\frac{3}{4}$, is not a whole number.
iv) $x^{-2}$ is not a polynomial, as the exponent, which is -2, is not a whole number .