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