Question

Which of the following is/are a polynomial?

• A. $x+y$
• B. $3\sqrt{x}+x^2$
• C. $2y+\frac{2}{y}$
• D. $xy$

Answer 1

Answer: (A), (D)

$xy$

For an algebraic expression to be a polynomial, the exponents on the variables must necessarily be whole numbers.

The expression $3\sqrt{x}+x^2$ can be written as $3x^{\frac{1}{2}}+x^2$.
The power on the variable $x$ in $3\sqrt{x}$ is $\frac{1}{2}$, which is not a whole number.
Thus, the expression $3\sqrt{x}+x^2$ is not a polynomial.

In the expression $2y+\frac{2}{y}$, the term $\frac{2}{y}$ can be written as $2y^{-1}$.
The power on the variable, $-1$, is not a whole number.
Thus, the expression $2y+\frac{2}{y}$ is not a polynomial.