Question

Identify the expression is a polynomial or not.
$7x^3-z^{\frac{1}{3}}+\frac{4}{y^3}$

• A. It is a polynomial expression.
• B. It is not a polynomial expression.

Answer 1

The correct option is B It is not a polynomial expression.

$7x^3-z^{\frac{1}{3}}+\frac{4}{y^3}$
$=7x^3-z^{\frac{1}{3}}+4y^{-3}$

1. The first term, $7x^3$, has unknown variable with exponent as whole number, i.e., 3.
2. However the second term, $z^{\frac{1}{3}}$, has a variable with exponent of $\frac{1}{3}$ which is not a whole number.
3. Also the third term, $4y^{-3}$, has a variable with $-3$ as exponent. $-3$ is not a whole number.

$\therefore$ As the expression has atleast one variable whose exponent is not a whole number, the expression is not a polynomial.