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Answer :
To determine which polynomial is in standard form, we need to write each polynomial with its terms in descending order based on the degree of each term. The degree of a term is the exponent of the variable, such as [tex]\(x\)[/tex].
Let's analyze each polynomial:
1. [tex]\(2x^4 + 8 + 24x^5\)[/tex]
- Rearrange the terms by the degree of [tex]\(x\)[/tex]: [tex]\(24x^5 + 2x^4 + 8\)[/tex].
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Rearrange the terms: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
3. [tex]\(19x + 6x^2 + 2\)[/tex]
- Rearrange the terms: [tex]\(6x^2 + 19x + 2\)[/tex].
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- It is already in the correct order by degrees: [tex]\(23x^9 - 12x^4 + 19\)[/tex].
The polynomial in standard form is [tex]\(23x^9 - 12x^4 + 19\)[/tex], because its terms are already arranged in descending order based on the degree of [tex]\(x\)[/tex].
Let's analyze each polynomial:
1. [tex]\(2x^4 + 8 + 24x^5\)[/tex]
- Rearrange the terms by the degree of [tex]\(x\)[/tex]: [tex]\(24x^5 + 2x^4 + 8\)[/tex].
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Rearrange the terms: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
3. [tex]\(19x + 6x^2 + 2\)[/tex]
- Rearrange the terms: [tex]\(6x^2 + 19x + 2\)[/tex].
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- It is already in the correct order by degrees: [tex]\(23x^9 - 12x^4 + 19\)[/tex].
The polynomial in standard form is [tex]\(23x^9 - 12x^4 + 19\)[/tex], because its terms are already arranged in descending order based on the degree of [tex]\(x\)[/tex].
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