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Identify polynomials in the given expressions.
a. $9 x+1$
b. $\frac{2}{x}-1$
c. $\frac{1}{b}+3$
d. $x-1$
e. 200
Given :
The given expressions are a. $9 x+1$
b. $\frac{2}{x}-1$
c. $\frac{1}{b}+3$
d. $x-1$
e. 200
To do :
We have to identify whether the given expressions are polynomials.
Solution :
Polynomials:
Polynomials are expressions in which each term is a constant multiplied by a variable raised to a whole number power.
a. In $9x+1$, the variables(x) in the terms are raised to a whole number power.
Therefore, $9x+1$ is a polynomial.
b. In $\frac{2}{x}-1$, the term $\frac{1}{x}$ is equal to $x^{-1}$ and in this term the variable x is raised to the power.
$-1$ is not a whole number.
Therefore, $\frac{2}{x}-1$ is not a polynomial.
c. In $\frac{1}{b}+3$, the term $\frac{1}{b}$ is equal to $b^{-1}$ and in this term, the variable b is raised to the power.
$-1$ is not a whole number.
Therefore, $\frac{1}{b}+3$ is not a polynomial.
d. In $x-1$, the variables(x) in the terms are raised to a whole number power.
Therefore, $x-1$ is a polynomial.
e. 200 can be written as $200x^0$.
Therefore, 200 is a polynomial.
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