Question

Justify if the expression $\frac{1}{-5x^2}+5x+7$is polynomial or not.

Answer 1

Define polynomial:

An algebraic expression where the exponents of the all the variables are in whole numbers. Means the power of the variables can be positive integers including zero but not fraction, decimals or negative integers.

In the given expression $\frac{1}{-5x^2}+5x+7$ that can be written as $-5x^{-2}+5x+7$, the exponents of variable are $-2$ , $1$ and $0$.

Since, $-2$ is not a whole number.

Hence,the expression is not a polynomial.