To determine which polynomial is already in standard form, we must verify that the polynomial's terms are ordered by descending powers of [tex]\(x\)[/tex]. Let's inspect each polynomial one by one:
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- Rearrange the terms in descending order: [tex]\(24x^5 + 2x^4 + 6\)[/tex]
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Rearrange the terms in descending order: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex]
3. [tex]\(19x + 6x^2 + 2\)[/tex]
- Rearrange the terms in descending order: [tex]\(6x^2 + 19x + 2\)[/tex]
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- This polynomial is already in descending order: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
The fourth polynomial, [tex]\(23x^9 - 12x^4 + 19\)[/tex], is already in standard form because its terms are ordered by descending powers of [tex]\(x\)[/tex].
Thus, the polynomial that is in standard form is the fourth one, and it corresponds to the answer index 3.
