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Identify polynomials in the following:$ f(x)=2+\frac{3}{x}+4 x $
Given:
\( f(x)=2+\frac{3}{x}+4 x \)
To do:
We have to check whether \( f(x)=2+\frac{3}{x}+4 x \) 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.
\( f(x)=2+\frac{3}{x}+4 x \) is not a polynom[Math Processing Error]ial because the term $\frac{3}{x}$ is equal to $3x^{-1}$ and in this term the variable $x$ is raised to the power $-1$ which is not a whole number.
Therefore, \( f(x)=2+\frac{3}{x}+4 x \) is not a polynomial.
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