Question

Identify the following as polynomial and hence write their degrees :

$5x^2-4x+3$

Answer 1

We have the algebraic expression :

$5x^2-4x+3$

Step 1: Identification of polynomial :

Since a polynomial is an algebraic expression in which powers of variables in each term are whole number.

In term-1 that is $5x^2$ , power of variable $x$ is 2 which is a whole number

In term-2 that is $-4x$ , power of variable $x$ is 1 which is a whole number

and term-3 that is $3$ which is a constant term

so power of all the variable in each term is whole number

Therefore, $\mathbf{5}{\mathit{x}}^{\mathbf{2}}\mathbf{}\mathbf{-}\mathbf{}\mathbf{4}\mathit{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{3}$ is a polynomial

Step 2: Finding degree of polynomial :

Since, Degree of a polynomial is the greatest sum of powers of the variables in a term.

Terms	$5x^2$	$-4x$	$3$
Degree	$2$ ( Maximum )	$1$	$0$

So maximum degree of each term of the given polynomial is $2$

Therefore, Degree of the polynomial $\mathbf{5}{\mathit{x}}^{\mathbf{2}}\mathbf{}\mathbf{-}\mathbf{}\mathbf{4}\mathit{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{3}$ is $\mathbf{2}$