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