Answer :
To determine which polynomial is in standard form, we need to look at the exponents of the terms. A polynomial is in standard form when its terms are arranged in descending order based on their degrees (the exponents of the variables).
Let's look at each polynomial:
1. Polynomial 1: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- Degrees of terms: 9, 4, 0
- This polynomial is in standard form because the terms are arranged in descending order of the exponents.
2. Polynomial 2: [tex]\(19x + 6x^2 + 2\)[/tex]
- Degrees of terms: 1, 2, 0
- This polynomial is not in standard form because the terms are not in descending order (the term [tex]\(6x^2\)[/tex] should be first).
3. Polynomial 3: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Degrees of terms: 2, 3, 4
- This polynomial is not in standard form because the terms are not in descending order (the term [tex]\(12x^4\)[/tex] should come first, followed by [tex]\(-9x^3\)[/tex], and then [tex]\(6x^2\)[/tex]).
4. Polynomial 4: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- Degrees of terms: 4, 0, 5
- This polynomial is not in standard form because the terms are not in descending order (the term [tex]\(24x^5\)[/tex] should be first).
Given the evaluations:
- Polynomial 1 is in standard form.
- Polynomials 2, 3, and 4 are not in standard form because they do not have their terms arranged from the highest degree to the lowest.
Therefore, based on this analysis, the polynomial [tex]\(23x^9 - 12x^4 + 19\)[/tex] is in standard form.
Let's look at each polynomial:
1. Polynomial 1: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- Degrees of terms: 9, 4, 0
- This polynomial is in standard form because the terms are arranged in descending order of the exponents.
2. Polynomial 2: [tex]\(19x + 6x^2 + 2\)[/tex]
- Degrees of terms: 1, 2, 0
- This polynomial is not in standard form because the terms are not in descending order (the term [tex]\(6x^2\)[/tex] should be first).
3. Polynomial 3: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Degrees of terms: 2, 3, 4
- This polynomial is not in standard form because the terms are not in descending order (the term [tex]\(12x^4\)[/tex] should come first, followed by [tex]\(-9x^3\)[/tex], and then [tex]\(6x^2\)[/tex]).
4. Polynomial 4: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- Degrees of terms: 4, 0, 5
- This polynomial is not in standard form because the terms are not in descending order (the term [tex]\(24x^5\)[/tex] should be first).
Given the evaluations:
- Polynomial 1 is in standard form.
- Polynomials 2, 3, and 4 are not in standard form because they do not have their terms arranged from the highest degree to the lowest.
Therefore, based on this analysis, the polynomial [tex]\(23x^9 - 12x^4 + 19\)[/tex] is in standard form.
