Answer :
To determine which polynomial is in standard form, we need to recall the definition of standard form for polynomials. A polynomial is in standard form when its terms are written in descending order of their degrees (the exponent of each term).
Let's examine each polynomial provided:
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- This polynomial is not in standard form because the terms are not in descending order of their degrees. The correct standard form should be [tex]\(24x^5 + 2x^4 + 6\)[/tex].
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- This polynomial is not in standard form because the terms are not in descending order of their degrees. The correct standard form should be [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
3. [tex]\(19x + 6x^2 + 2\)[/tex]
- This polynomial is not in standard form because the terms are not in descending order of their degrees. The correct standard form should be [tex]\(6x^2 + 19x + 2\)[/tex].
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- This polynomial is already in standard form because the terms are arranged in descending order of their degrees: [tex]\(9, 4, \)[/tex] and [tex]\(0\)[/tex].
Based on the analysis above, the polynomial in standard form is:
[tex]\[ 23x^9 - 12x^4 + 19 \][/tex]
Thus, the correct answer is the fourth polynomial [tex]\(23x^9 - 12x^4 + 19\)[/tex].
Let's examine each polynomial provided:
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- This polynomial is not in standard form because the terms are not in descending order of their degrees. The correct standard form should be [tex]\(24x^5 + 2x^4 + 6\)[/tex].
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- This polynomial is not in standard form because the terms are not in descending order of their degrees. The correct standard form should be [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
3. [tex]\(19x + 6x^2 + 2\)[/tex]
- This polynomial is not in standard form because the terms are not in descending order of their degrees. The correct standard form should be [tex]\(6x^2 + 19x + 2\)[/tex].
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- This polynomial is already in standard form because the terms are arranged in descending order of their degrees: [tex]\(9, 4, \)[/tex] and [tex]\(0\)[/tex].
Based on the analysis above, the polynomial in standard form is:
[tex]\[ 23x^9 - 12x^4 + 19 \][/tex]
Thus, the correct answer is the fourth polynomial [tex]\(23x^9 - 12x^4 + 19\)[/tex].
