Question

Identify the following as polynomial and hence write their degrees :

$x^2+\frac{x{y}^3}{2}-\frac{1}{3}$

Answer 1

Step 1: Identification of polynomial :

We have the algebraic expression :

$x^2+\frac{x{y}^3}{2}-\frac{1}{3}$

Since a polynomial is an algebraic expression in which powers of variables in each term are whole number.

In term-1 that is $x^2$ , power of variable is $2$ which is a whole number

In term-2 that is $\frac{x{y}^3}{2}$ , power of variable $x$ is $1$ & power of variable $y$ is $3$ which are a whole numbers

Term-3 is $-\frac{1}{3}$, which is a constant term

So power of all the variable in each term is whole number

Therefore, $x^2+\frac{{\mathrm{xy}}^3}{2}-\frac{1}{3}$ is a polynomial

Step 2 Finding degree of polynomial :

Since, degree of a polynomial is the greatest sum of powers of the variables in a term.

Terms	$x^2$	$\frac{x{y}^3}{2}$	$-\frac{1}{3}$
Degree	$2$	$1+3=4$ (Maximum)	$0$

So maximum degree of the given polynomial is $4$

Therefore, degree of the polynomial $x^2+\frac{{\mathrm{xy}}^3}{2}-\frac{1}{3}$ is $\mathbf{4}$