A polynomial is defined as an expression that consists of variables raised to non-negative integer powers and has coefficients that are real or complex numbers. Based on this definition, let's analyze each of the expressions you provided:
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\(x^2 + 2\): This is a polynomial. It consists of a term \(x^2\) (which has a non-negative integer exponent) and a constant term \(2\).
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\(7x^7 - 2x^{-4} + 3\): This is not a polynomial because of the term \(-2x^{-4}\). The exponent \(-4\) is negative, which disqualifies this expression from being a polynomial.
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\(1/x - 1\): This is also not a polynomial. The term \(1/x\) can be rewritten as \(x^{-1}\), which has a negative exponent.
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\(x^8 - 2/x^{-2} + 3\): This is not a polynomial either because of the term \(-2/x^{-2}\), which can be rewritten as \(-2x^2\), but it originally involves division by \(x\) or negative exponents.
In conclusion, the only polynomial in your list is:
\(x^2 + 2\).