Question

Identify the algebraic expression is polynomial. If so write their degree.

$3x^2+\frac{2}{x}-3$

Answer 1

We have $3x^2+\frac{2}{x}-3$

An algebraic expression containing only one variable is called a polynomial in that variable if the powers of the variable in each term are non-negative integral powers.

Thus, an algebraic expression of the form $a+bx+c{x}^2+d{x}^3+...,$ where $a,b,c,d...$are constants and $x$is a variable is called a polynomial in the variable $x$.

No term in a polynomial can be of the form $\frac{1}{x},\frac{1}{x^2},\frac{x}{y}\mathrm{etc}.$

Therefore, $3x^2+\frac{2}{x}-3$ is not a polynomial, because it has the form of $\frac{2}{x}=2\times \frac{1}{x}$.