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Answer :
To determine which polynomial is written in standard form, let's first understand what "standard form" means for polynomials. A polynomial is in standard form when its terms are written in descending order of their exponents.
Let's look at the given polynomial options:
1. [tex]\(8x^2 + 9x^3 - 11 - 3x\)[/tex]
2. [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
3. [tex]\(-11 - 3x + 8x^2 + 9x^3\)[/tex]
4. [tex]\(-3x + 8x^2 + 9x^3 - 11\)[/tex]
We'll analyze each option to determine which one is already in the standard form:
1. Option 1: [tex]\(8x^2 + 9x^3 - 11 - 3x\)[/tex]
- When reordering by exponents: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
- Resulting form: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
2. Option 2: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
- Already in order by exponents (descending order).
3. Option 3: [tex]\(-11 - 3x + 8x^2 + 9x^3\)[/tex]
- When reordered by exponents: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
- Resulting form: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
4. Option 4: [tex]\(-3x + 8x^2 + 9x^3 - 11\)[/tex]
- Reordered by exponents: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
- Resulting form: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
Based on our analysis, Option 2 is already in standard form as [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex], with the polynomial terms arranged in descending order. Therefore, Option 2 is the correct answer.
Let's look at the given polynomial options:
1. [tex]\(8x^2 + 9x^3 - 11 - 3x\)[/tex]
2. [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
3. [tex]\(-11 - 3x + 8x^2 + 9x^3\)[/tex]
4. [tex]\(-3x + 8x^2 + 9x^3 - 11\)[/tex]
We'll analyze each option to determine which one is already in the standard form:
1. Option 1: [tex]\(8x^2 + 9x^3 - 11 - 3x\)[/tex]
- When reordering by exponents: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
- Resulting form: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
2. Option 2: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
- Already in order by exponents (descending order).
3. Option 3: [tex]\(-11 - 3x + 8x^2 + 9x^3\)[/tex]
- When reordered by exponents: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
- Resulting form: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
4. Option 4: [tex]\(-3x + 8x^2 + 9x^3 - 11\)[/tex]
- Reordered by exponents: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
- Resulting form: [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex]
Based on our analysis, Option 2 is already in standard form as [tex]\(9x^3 + 8x^2 - 3x - 11\)[/tex], with the polynomial terms arranged in descending order. Therefore, Option 2 is the correct answer.
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