Asked by pooop
which of the following is a polynomial x^2+2, 7x^7-2x^-4+3, 1/x-1, x^8-2/x^-2+3
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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:
1. **\(x^2 + 2\)**: This is a polynomial. It consists of a term \(x^2\) (which has a non-negative integer exponent) and a constant term \(2\).
2. **\(7x^7 - 2x^{-4} + 3\)**: This is **not** a polynomial because of the term \(-2x^{-4}\). The exponent \(-4\) is negative, which disqualifies this expression from being a polynomial.
3. **\(1/x - 1\)**: This is also **not** a polynomial. The term \(1/x\) can be rewritten as \(x^{-1}\), which has a negative exponent.
4. **\(x^8 - 2/x^{-2} + 3\)**: 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:
**\(x^2 + 2\)**.
1. **\(x^2 + 2\)**: This is a polynomial. It consists of a term \(x^2\) (which has a non-negative integer exponent) and a constant term \(2\).
2. **\(7x^7 - 2x^{-4} + 3\)**: This is **not** a polynomial because of the term \(-2x^{-4}\). The exponent \(-4\) is negative, which disqualifies this expression from being a polynomial.
3. **\(1/x - 1\)**: This is also **not** a polynomial. The term \(1/x\) can be rewritten as \(x^{-1}\), which has a negative exponent.
4. **\(x^8 - 2/x^{-2} + 3\)**: 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:
**\(x^2 + 2\)**.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.