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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.
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