Answer :
To determine which polynomial is in standard form, we need to understand what standard form means for polynomials. A polynomial is in standard form when its terms are arranged in descending order of their exponents, from the highest to the lowest. Let's examine each option:
1. Option 1: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- In standard form, the terms should be ordered from the highest degree to the lowest. Rearranging this gives us: [tex]\(24x^5 + 2x^4 + 6\)[/tex].
2. Option 2: [tex]\(x^2 - 9x^3 + 12x^4\)[/tex]
- Rearranging gives: [tex]\(12x^4 - 9x^3 + x^2\)[/tex].
3. Option 3: [tex]\(19x + 6x^2 + 2\)[/tex]
- Rearranging gives: [tex]\(6x^2 + 19x + 2\)[/tex].
4. Option 4: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- This polynomial is already in standard form because the terms are ordered from the highest exponent (9) to the lowest (a constant term).
Therefore, the polynomial that is already in standard form from the options given is Option 4: [tex]\(23x^9 - 12x^4 + 19\)[/tex].
1. Option 1: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- In standard form, the terms should be ordered from the highest degree to the lowest. Rearranging this gives us: [tex]\(24x^5 + 2x^4 + 6\)[/tex].
2. Option 2: [tex]\(x^2 - 9x^3 + 12x^4\)[/tex]
- Rearranging gives: [tex]\(12x^4 - 9x^3 + x^2\)[/tex].
3. Option 3: [tex]\(19x + 6x^2 + 2\)[/tex]
- Rearranging gives: [tex]\(6x^2 + 19x + 2\)[/tex].
4. Option 4: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- This polynomial is already in standard form because the terms are ordered from the highest exponent (9) to the lowest (a constant term).
Therefore, the polynomial that is already in standard form from the options given is Option 4: [tex]\(23x^9 - 12x^4 + 19\)[/tex].
