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Answer :
To determine which polynomial is in standard form, we need to look at the order of the terms in each polynomial. A polynomial is in standard form when its terms are arranged in descending order of their exponents (from the highest degree to the lowest degree).
Let's evaluate each polynomial individually:
1. Polynomial 1: [tex]\(2x^4 + 8 + 24x^5\)[/tex]
- Rearrange the terms based on the degree of [tex]\(x\)[/tex]:
[tex]\(24x^5 + 2x^4 + 8\)[/tex].
- This polynomial is not in standard form because its terms were initially not in descending order.
2. Polynomial 2: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Rearrange the terms based on the degree of [tex]\(x\)[/tex]:
[tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
- This polynomial is not in standard form because its terms were initially not in descending order.
3. Polynomial 3: [tex]\(18x + 6x^2 + 2\)[/tex]
- Rearrange the terms based on the degree of [tex]\(x\)[/tex]:
[tex]\(6x^2 + 18x + 2\)[/tex].
- This polynomial is not in standard form because its terms were initially not in descending order.
4. Polynomial 4: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- Check the existing order: The terms are already ordered from the highest to the lowest degree: [tex]\(23x^9\)[/tex], [tex]\( - 12x^4\)[/tex], and a constant [tex]\(19\)[/tex].
- This polynomial is already in standard form.
Therefore, the polynomial that is in standard form is the fourth one: [tex]\(23x^9 - 12x^4 + 19\)[/tex].
Let's evaluate each polynomial individually:
1. Polynomial 1: [tex]\(2x^4 + 8 + 24x^5\)[/tex]
- Rearrange the terms based on the degree of [tex]\(x\)[/tex]:
[tex]\(24x^5 + 2x^4 + 8\)[/tex].
- This polynomial is not in standard form because its terms were initially not in descending order.
2. Polynomial 2: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Rearrange the terms based on the degree of [tex]\(x\)[/tex]:
[tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
- This polynomial is not in standard form because its terms were initially not in descending order.
3. Polynomial 3: [tex]\(18x + 6x^2 + 2\)[/tex]
- Rearrange the terms based on the degree of [tex]\(x\)[/tex]:
[tex]\(6x^2 + 18x + 2\)[/tex].
- This polynomial is not in standard form because its terms were initially not in descending order.
4. Polynomial 4: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- Check the existing order: The terms are already ordered from the highest to the lowest degree: [tex]\(23x^9\)[/tex], [tex]\( - 12x^4\)[/tex], and a constant [tex]\(19\)[/tex].
- This polynomial is already in standard form.
Therefore, the polynomial that is in standard form is the fourth one: [tex]\(23x^9 - 12x^4 + 19\)[/tex].
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