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Answer :
To determine which polynomial is in standard form, we need to arrange the terms in descending order based on their exponents. This means we should start from the highest degree term (largest exponent) and proceed to the lowest. Let's examine each option:
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]:
- Rearrange terms by degree: [tex]\(24x^5 + 2x^4 + 6\)[/tex].
- This polynomial is not initially in standard form.
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]:
- Rearrange terms by degree: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
- This polynomial is not initially in standard form.
3. [tex]\(19x + 6x^2 + 2\)[/tex]:
- Rearrange terms by degree: [tex]\(6x^2 + 19x + 2\)[/tex].
- This polynomial is initially not in standard form.
4. [tex]\(23x^3 - 12x^4 + 19\)[/tex]:
- Rearrange terms by degree: [tex]\(-12x^4 + 23x^3 + 19\)[/tex].
- This polynomial is not initially in standard form.
Now, by examining the polynomials and doing the rearrangement, we see that the third choice:
(19x + 6x^2 + 2) → 6x^2 + 19x + 2
This polynomial is already arranged in standard form: [tex]\(6x^2 + 19x + 2\)[/tex].
Therefore, the polynomial that is in standard form is [tex]\(19x + 6x^2 + 2\)[/tex] when rearranged correctly as [tex]\(6x^2 + 19x + 2\)[/tex].
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]:
- Rearrange terms by degree: [tex]\(24x^5 + 2x^4 + 6\)[/tex].
- This polynomial is not initially in standard form.
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]:
- Rearrange terms by degree: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
- This polynomial is not initially in standard form.
3. [tex]\(19x + 6x^2 + 2\)[/tex]:
- Rearrange terms by degree: [tex]\(6x^2 + 19x + 2\)[/tex].
- This polynomial is initially not in standard form.
4. [tex]\(23x^3 - 12x^4 + 19\)[/tex]:
- Rearrange terms by degree: [tex]\(-12x^4 + 23x^3 + 19\)[/tex].
- This polynomial is not initially in standard form.
Now, by examining the polynomials and doing the rearrangement, we see that the third choice:
(19x + 6x^2 + 2) → 6x^2 + 19x + 2
This polynomial is already arranged in standard form: [tex]\(6x^2 + 19x + 2\)[/tex].
Therefore, the polynomial that is in standard form is [tex]\(19x + 6x^2 + 2\)[/tex] when rearranged correctly as [tex]\(6x^2 + 19x + 2\)[/tex].
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