Identify polynomials in the following:$ p(x)=\frac{2}{3} x^{2}-\frac{7}{4} x+9 $
Given:
\( p(x)=\frac{2}{3} x^{2}-\frac{7}{4} x+9 \)
To do:
We have to check whether \( p(x)=\frac{2}{3} x^{2}-\frac{7}{4} x+9 \) 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 \( p(x)=\frac{2}{3} x^{2}-\frac{7}{4} x+9 \), $x$ is raised to the powers $2$ and $1$ which are whole numbers.
Therefore, \( p(x)=\frac{2}{3} x^{2}-\frac{7}{4} x+9 \) is a polynomial.
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