Question
which of the following is monomial 20x^11, 20x^11-30, 11x-9, 9/x
Answers
GPT-4o mini
A monomial is a polynomial with just one term. Let's analyze each of the given options:
1. **20x^11**: This is a single term, so it is a monomial.
2. **20x^11 - 30**: This has two terms (20x^11 and -30), so it is not a monomial.
3. **11x - 9**: This also has two terms (11x and -9), so it is not a monomial.
4. **9/x**: This can be rewritten as \(9x^{-1}\), which is a single term but involves a negative exponent, making it behave differently than a standard polynomial term. However, since it only has one term, you could argue that it is a monomial depending on the context of whether you allow negative exponents.
Therefore, the primary monomial from your options is **20x^11**. If you're strictly following the definition of a polynomial (which does not allow negative or fractional exponents), then only **20x^11** would qualify as a monomial.
1. **20x^11**: This is a single term, so it is a monomial.
2. **20x^11 - 30**: This has two terms (20x^11 and -30), so it is not a monomial.
3. **11x - 9**: This also has two terms (11x and -9), so it is not a monomial.
4. **9/x**: This can be rewritten as \(9x^{-1}\), which is a single term but involves a negative exponent, making it behave differently than a standard polynomial term. However, since it only has one term, you could argue that it is a monomial depending on the context of whether you allow negative exponents.
Therefore, the primary monomial from your options is **20x^11**. If you're strictly following the definition of a polynomial (which does not allow negative or fractional exponents), then only **20x^11** would qualify as a monomial.