Question

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

$\frac{2}{5}-\frac{3}{7}{x}^3+5x{y}^3-\frac{1}{2}{z}^5$

Answer 1

Finding whether $\frac{2}{5}-\frac{3}{7}{x}^3+5x{y}^3-\frac{1}{2}{z}^5$ 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, $\frac{2}{5}-\frac{3}{7}{x}^3+5x{y}^3-\frac{1}{2}{z}^5$ is a polynomial.

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

Since, the constant are $\frac{2}{5},-\frac{3}{7},5,-\frac{1}{2}$ and variable are $x^3,x{y}^3,z^5$

Hence ,The degree of expression $\frac{2}{5}-\frac{3}{7}{x}^3+5x{y}^3-\frac{1}{2}{z}^5$ is $5$.