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Answer :
A polynomial is said to be in standard form when its terms are arranged in descending order of their exponents.
Let's examine each polynomial and arrange its terms in descending order of exponents:
1. First Polynomial: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- Rearranged: [tex]\(24x^5 + 2x^4 + 6\)[/tex]
2. Second Polynomial: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Rearranged: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex]
3. Third Polynomial: [tex]\(19x + 6x^2 + 2\)[/tex]
- Rearranged: [tex]\(6x^2 + 19x + 2\)[/tex]
4. Fourth Polynomial: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- Rearranged: [tex]\(23x^9 - 12x^4 + 19\)[/tex] (already in standard form)
After rearranging, we can see that only the fourth polynomial [tex]\(23x^9 - 12x^4 + 19\)[/tex] is already in standard form.
Therefore, the fourth polynomial is in standard form:
[tex]\[23x^9 - 12x^4 + 19\][/tex]
Let's examine each polynomial and arrange its terms in descending order of exponents:
1. First Polynomial: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- Rearranged: [tex]\(24x^5 + 2x^4 + 6\)[/tex]
2. Second Polynomial: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Rearranged: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex]
3. Third Polynomial: [tex]\(19x + 6x^2 + 2\)[/tex]
- Rearranged: [tex]\(6x^2 + 19x + 2\)[/tex]
4. Fourth Polynomial: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- Rearranged: [tex]\(23x^9 - 12x^4 + 19\)[/tex] (already in standard form)
After rearranging, we can see that only the fourth polynomial [tex]\(23x^9 - 12x^4 + 19\)[/tex] is already in standard form.
Therefore, the fourth polynomial is in standard form:
[tex]\[23x^9 - 12x^4 + 19\][/tex]
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