Question

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

$\frac{2}{3}{x}^2-\frac{5}{7}x-\frac{1}{4}$

Answer 1

We have $\frac{2}{3}{x}^2-\frac{5}{7}x-\frac{1}{4}$

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, $\frac{2}{3}{x}^2-\frac{5}{7}x-\frac{1}{4}$ is a polynomial.

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

Since the constant are $a=\frac{2}{3},b=-\frac{5}{7},c=-\frac{1}{4}$ and variable are $x^2-x$

Hence, the degree of expression $\frac{2}{3}{x}^2-\frac{5}{7}x-\frac{1}{4}$ is $2$.