Question

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

$2-z^3+3xy+\frac{1}{2}{x}^4$

Answer 1

Finding whether $2-z^3+3xy+\frac{1}{2}{x}^4$ is polynomial or not .

An algebraic expression containing only one variable is called a polynomial in that variable if the powers of the variable in each term are non- negative integral powers .

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 $x$.

Therefore, $2-z^3+3xy+\frac{1}{2}{x}^4$ is a polynomial.

now, The greatest power of $x$ present in the polynomial is called the degree of the polynomial .

Since, the constant are $2,-1,3,\frac{1}{2}$ and variable are $z^3,xy,x^4$

Hence ,The degree of expression $2-z^3+3xy+\frac{1}{2}{x}^4$ is $4$.