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Answer :
To determine which polynomials are in standard form, we need to understand what "standard form" means for polynomials.
A polynomial is in standard form when its terms are arranged in descending order of their degree (highest power of [tex]\(x\)[/tex]). Let's look at each polynomial given:
1. [tex]\(2x^4 + 0.6 + 24x^5\)[/tex]
- This polynomial has terms: [tex]\(24x^5\)[/tex], [tex]\(2x^4\)[/tex], and [tex]\(0.6\)[/tex].
- It should be ordered as: [tex]\(24x^5 + 2x^4 + 0.6\)[/tex].
- The terms are currently not in descending order (degree 5 term should come first).
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- This polynomial has terms: [tex]\(12x^4\)[/tex], [tex]\(-9x^3\)[/tex], and [tex]\(6x^2\)[/tex].
- It can be ordered as: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
- The terms are not currently in descending order, but they can be rearranged to be in standard form.
3. [tex]\(19x + 6x^2 + 2\)[/tex]
- This polynomial has terms: [tex]\(6x^2\)[/tex], [tex]\(19x\)[/tex], and [tex]\(2\)[/tex].
- It should be ordered as: [tex]\(6x^2 + 19x + 2\)[/tex].
- Currently, it is not in descending order of degree (degree 2 should come first).
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- This polynomial has terms: [tex]\(23x^9\)[/tex], [tex]\(-12x^4\)[/tex], and [tex]\(19\)[/tex].
- The terms are already in descending order: [tex]\(23x^9 - 12x^4 + 19\)[/tex].
Based on this analysis, polynomials 2 and 4 are in standard form because either they can be rearranged or are already correctly ordered by decreasing degree.
A polynomial is in standard form when its terms are arranged in descending order of their degree (highest power of [tex]\(x\)[/tex]). Let's look at each polynomial given:
1. [tex]\(2x^4 + 0.6 + 24x^5\)[/tex]
- This polynomial has terms: [tex]\(24x^5\)[/tex], [tex]\(2x^4\)[/tex], and [tex]\(0.6\)[/tex].
- It should be ordered as: [tex]\(24x^5 + 2x^4 + 0.6\)[/tex].
- The terms are currently not in descending order (degree 5 term should come first).
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- This polynomial has terms: [tex]\(12x^4\)[/tex], [tex]\(-9x^3\)[/tex], and [tex]\(6x^2\)[/tex].
- It can be ordered as: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
- The terms are not currently in descending order, but they can be rearranged to be in standard form.
3. [tex]\(19x + 6x^2 + 2\)[/tex]
- This polynomial has terms: [tex]\(6x^2\)[/tex], [tex]\(19x\)[/tex], and [tex]\(2\)[/tex].
- It should be ordered as: [tex]\(6x^2 + 19x + 2\)[/tex].
- Currently, it is not in descending order of degree (degree 2 should come first).
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- This polynomial has terms: [tex]\(23x^9\)[/tex], [tex]\(-12x^4\)[/tex], and [tex]\(19\)[/tex].
- The terms are already in descending order: [tex]\(23x^9 - 12x^4 + 19\)[/tex].
Based on this analysis, polynomials 2 and 4 are in standard form because either they can be rearranged or are already correctly ordered by decreasing degree.
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