To determine which polynomial is in standard form, we need to ensure that the terms are arranged in descending order of their degrees. Let's analyze each polynomial step-by-step:
1. Polynomial: \(2x^4 + 6 + 24x^5\)
- Terms: \(24x^5\), \(2x^4\), \(6\)
- Degrees: 5, 4, 0
- Ordered degrees should be: 5, 4, 0
- Analysis: The given polynomial is not in standard form because the degree of the terms should be arranged in descending order but here \(24x^5\) comes after \(2x^4\).
2. Polynomial: \(6x^2 - 9x^3 + 12x^4\)
- Terms: \(12x^4\), \(-9x^3\), \(6x^2\)
- Degrees: 4, 3, 2
- Ordered degrees should be: 4, 3, 2
- Analysis: The given polynomial is not in standard form because the term \(6x^2\) with degree 2 is written before \(-9x^3\) with degree 3 and \(12x^4\) with degree 4.
3. Polynomial: \(19x + 6x^2 + 2\)
- Terms: \(6x^2\), \(19x\), \(2\)
- Degrees: 2, 1, 0
- Ordered degrees should be: 2, 1, 0
- Analysis: The given polynomial is not in standard form because it should start with the highest degree, \(6x^2\), followed by the next degree term, \(19x\), and finally the constant term \(2\).
4. Polynomial: \(23x^9 - 12x^4 + 19\)
- Terms: \(23x^9\), \(-12x^4\), \(19\)
- Degrees: 9, 4, 0
- Ordered degrees should be: 9, 4, 0
- Analysis: The given polynomial is not in standard form because the degree of the terms \(23x^9\) is greater than the other terms. It satisfies the descending order condition properly with degrees 9, 4, and then 0.
After analyzing all the polynomials:
- None of the given polynomials are in standard form.
