Question

Identify which of the following algebraic expressions are polynomials. If so, write their degrees.

$xy+\frac{1}{x}+\frac{1}{y}$

Answer 1

Given algebraic expression is $xy+\frac{1}{x}+\frac{1}{y}$

An algebraic expression is said to be a polynomial if the power of its variable is either zero or positive in all terms.

Here, the algebraic expression $xy+\frac{1}{x}+\frac{1}{y}$ is the variable of $x$and$y$

So, the power of the term $xy=1+1=2$

the power of $x$in the term $\frac{1}{x^{}}=-1$

the power of $y$in the term $\frac{1}{y}=-1$

Since, the power in the term $\frac{1}{x},\frac{1}{y}$is $-1$which is negative.

Hence, it is not a polynomial.