Question
Which is a polynomial
1/x-1
(x^8-2)/(x^-2+3)
x^2+2
7x^7-2x^-4+3
1/x-1
(x^8-2)/(x^-2+3)
x^2+2
7x^7-2x^-4+3
Answers
GPT-4o mini
To determine which of the given expressions is a polynomial, we need to recall that a polynomial is defined as an expression that consists of variables raised to non-negative integer exponents, with coefficients that are real numbers.
Let's analyze each option:
1. \( \frac{1}{x} - 1 \)
This is not a polynomial because \( \frac{1}{x} \) can be rewritten as \( x^{-1} \), which has a negative exponent.
2. \( \frac{x^8 - 2}{x^{-2} + 3} \)
This is also not a polynomial because the denominator \( x^{-2} + 3 \) includes a term with a negative exponent.
3. \( x^2 + 2 \)
This is a polynomial because both terms \( x^2 \) and \( 2 \) (which can be considered \( 2x^0 \)) have non-negative integer exponents.
4. \( 7x^7 - 2x^{-4} + 3 \)
This is not a polynomial because \( -2x^{-4} \) has a negative exponent.
Among the options provided, the only polynomial is:
**\( x^2 + 2 \)**.
Let's analyze each option:
1. \( \frac{1}{x} - 1 \)
This is not a polynomial because \( \frac{1}{x} \) can be rewritten as \( x^{-1} \), which has a negative exponent.
2. \( \frac{x^8 - 2}{x^{-2} + 3} \)
This is also not a polynomial because the denominator \( x^{-2} + 3 \) includes a term with a negative exponent.
3. \( x^2 + 2 \)
This is a polynomial because both terms \( x^2 \) and \( 2 \) (which can be considered \( 2x^0 \)) have non-negative integer exponents.
4. \( 7x^7 - 2x^{-4} + 3 \)
This is not a polynomial because \( -2x^{-4} \) has a negative exponent.
Among the options provided, the only polynomial is:
**\( x^2 + 2 \)**.