Question

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

$\frac{2}{3}x{y}^2-5xy+\frac{3}{5}{x}^2{y}^2+2x$

Answer 1

Indentifying the algebraic expression and finding its degree

The given aalgebraic expression is $\frac{2}{3}x{y}^2-5xy+\frac{3}{5}{x}^2{y}^2+2x$

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.

As the exponents of all variables are whole numbers in given expression.

Therefore, $\frac{2}{3}x{y}^2-5xy+\frac{3}{5}{x}^2{y}^2+2x$ is a polynomial.

Now, the greatest power of variable present in the polynomial is called the degree of the polynomial .

Variables in given expression are $x{y}^2,xy,x^2{y}^2,x$ in which $x^2{y}^2$has highest power i.e., $2+2=4$

Hence ,the algebraic expression $\frac{2}{3}x{y}^2-5xy+\frac{3}{5}{x}^2{y}^2+2x$ is a polynomial of degree $4$.