Question

Identify algebraic expression is polynomial . if so, write their degree.

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

Answer 1

We have $\frac{2}{5}{x}^3-7x^2-\frac{1}{2}x+3$

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

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

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

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