To determine which polynomials are in standard form, we need to examine each polynomial and check if the terms are arranged in descending order of their degrees.
1. Polynomial: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- Terms: [tex]\(24x^5\)[/tex], [tex]\(2x^4\)[/tex], [tex]\(6\)[/tex]
- Degrees: 5, 4, 0
The degrees are 5, 4, and 0, which are in descending order. Thus, this polynomial is in standard form.
2. Polynomial: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Terms: [tex]\(12x^4\)[/tex], [tex]\(-9x^3\)[/tex], [tex]\(6x^2\)[/tex]
- Degrees: 4, 3, 2
The degrees are 4, 3, and 2, which are in descending order. Thus, this polynomial is in standard form.
3. Polynomial: [tex]\(19x + 6x^2 + 2\)[/tex]
- Terms: [tex]\(6x^2\)[/tex], [tex]\(19x\)[/tex], [tex]\(2\)[/tex]
- Degrees: 2, 1, 0
The degrees are 2, 1, and 0, which are in descending order. Thus, this polynomial is in standard form.
4. Polynomial: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- Terms: [tex]\(23x^9\)[/tex], [tex]\(-12x^4\)[/tex], [tex]\(19\)[/tex]
- Degrees: 9, 4, 0
The degrees are 9, 4, and 0, which are in descending order. Thus, this polynomial is in standard form.
Based on this analysis, the polynomials that are in standard form are:
[tex]\[ 2x^4 + 6 + 24x^5 \][/tex]
[tex]\[ 6x^2 - 9x^3 + 12x^4 \][/tex]
[tex]\[ 19x + 6x^2 + 2 \][/tex]
[tex]\[ 23x^9 - 12x^4 + 19 \][/tex]
So, the polynomials in standard form correspond to:
1. Polynomial [tex]\(2x^4 + 6 + 24x^5\)[/tex] is NOT in standard form.
2. Polynomial [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex] is in standard form.
3. Polynomial [tex]\(19x + 6x^2 + 2\)[/tex] is in standard form.
4. Polynomial [tex]\(23x^9 - 12x^4 + 19\)[/tex] is in standard form.
Therefore, the polynomials in standard form are the 2nd, 3rd, and 4th polynomials.
