Question

Identify the algebraic expression is polynomials. If so, write their degree .

$xy+\frac{x}{y}-7$

Answer 1

Finding whether $xy+\frac{x}{y}-7$ is polynomial or not .

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer

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 $\frac{1}{x},\frac{1}{y},\frac{1}{x^2},\frac{x}{y}etc$

Therefore, $xy+\frac{x}{y}-7=xy+x{y}^{-1}-7$ is not a polynomial because the exponent of variable $y$ is negative.

Hence, it has no degree .