Identify polynomials in the following:$ f(x)=4 x^{3}-x^{2}-3 x+7 $

Given:

\( f(x)=4 x^{3}-x^{2}-3 x+7 \)

To do:

We have to check whether \( f(x)=4 x^{3}-x^{2}-3 x+7 \) is a polynomial.

Solution:

Polynomials: 

Polynomials are expressions in which each term is a constant multiplied by a variable raised to a whole number power.

To identify whether the given expression is polynomial, check if all the powers of the variables are whole numbers after simplification. If any of the powers is a fraction or negative integer then it is not a polynomial.

In \( f(x)=4 x^{3}-x^{2}-3 x+7 \), $x$ is raised to the powers $3, 2$ and $1$ which are whole numbers.

Therefore, \( f(x)=4 x^{3}-x^{2}-3 x+7 \) is a polynomial.