Answer :
To determine which polynomial is in standard form, you need to check if each polynomial is ordered by the powers of the variable from the highest to the lowest power. Let's go through each option:
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- This polynomial is not in standard form. The terms are not in order of decreasing exponents. The correct order 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 exponents are out of order. It should be arranged as [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
3. [tex]\(19x + 6x^2 + 2\)[/tex]
- This is not in standard form since the terms are not in decreasing order. The correct arrangement is [tex]\(6x^2 + 19x + 2\)[/tex].
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- This polynomial is in standard form because the terms are correctly ordered from highest to lowest power: [tex]\(23x^9 - 12x^4 + 19\)[/tex].
After examining all the options, the polynomial [tex]\(23x^9 - 12x^4 + 19\)[/tex] is the one in standard form.
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- This polynomial is not in standard form. The terms are not in order of decreasing exponents. The correct order 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 exponents are out of order. It should be arranged as [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
3. [tex]\(19x + 6x^2 + 2\)[/tex]
- This is not in standard form since the terms are not in decreasing order. The correct arrangement is [tex]\(6x^2 + 19x + 2\)[/tex].
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- This polynomial is in standard form because the terms are correctly ordered from highest to lowest power: [tex]\(23x^9 - 12x^4 + 19\)[/tex].
After examining all the options, the polynomial [tex]\(23x^9 - 12x^4 + 19\)[/tex] is the one in standard form.
