Question

Following algebraic expression is polynomial or not? If so, write the degree.

$x^3-3xy+x^2{y}^2$

Answer 1

Checking whether the algebraic expression is polynomial or not

Given algebraic expression $x^3-3xy+x^2{y}^2$

It is an algebraic expression of variable $x,y$

An algebraic expression is said to be a polynomial if the power of the variable is non-negative.

The power of the variables is positive in an algebraic expression $x^3-3xy+x^2{y}^2$

Thus, it is a polynomial.

Since,

Degree of term $x^3=3$

Degree of term $-3xy=1+1=2$

Degree of term $x^2{y}^2=2+2=4$

Therefore,

Maximum degree $=4$

Thus, the degree of the polynomial $x^3-3xy+x^2{y}^2$ is $4$

Hence, given algebraic expression is a polynomial of degree four.