Examples

x^{2} - 4 x^{- 2} + 1

$x^{2} - 4 x^{- 2} + 1$

Step 1

A polynomial is a combination of terms separated using

+

$+$ or

-

$-$ signs. Polynomials cannot contain any of the following:

1. Variables raised to a negative or fractional exponent. (

2 x^{- 2}

$2 x^{- 2}$ ,

x^{\frac{1}{2}}

$x^{\frac{1}{2}}$ ,

\dots

$\dots$ ).

2. Variables in the denominator. (

\frac{1}{x}

$\frac{1}{x}$ ,

\frac{1}{x^{2}}

$\frac{1}{x^{2}}$ ,

\dots

$\dots$ ).

3. Variables under a radical. (

\sqrt{x}

$\sqrt{x}$ ,

\sqrt[3]{x}

$\sqrt[3]{x}$ ,

\dots

$\dots$ ).

4. Special features. (trig functions, absolute values, logarithms,

\dots

$\dots$ ).

Step 2

Determine if the expression breaks any of the rules.

Breaks rule

1

$1$

Step 3

Determine if the expression is a polynomial.

Not a polynomial

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