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Answer :
Sure! Let's figure out which polynomial is in standard form. A polynomial is in standard form when its terms are ordered from the highest degree to the lowest degree.
Here are the given polynomials:
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
3. [tex]\(19x + 6x^2 + 2\)[/tex]
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]
Let's examine each one to check if it's in standard form:
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]: The terms arranged by degrees are [tex]\(24x^5\)[/tex], [tex]\(2x^4\)[/tex], and the constant 6. Currently, it's not in standard form because the highest degree term [tex]\(24x^5\)[/tex] is not written first.
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]: The correct order from highest to lowest degree should be [tex]\(12x^4\)[/tex], [tex]\(-9x^3\)[/tex], and [tex]\(6x^2\)[/tex]. It's not in standard form as written.
3. [tex]\(19x + 6x^2 + 2\)[/tex]: The terms arranged in standard form should have been [tex]\(6x^2\)[/tex], [tex]\(19x\)[/tex], and 2. So, this is also not in standard form as given.
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]: This polynomial is already in standard form, with the degrees in descending order: [tex]\(23x^9\)[/tex], [tex]\(-12x^4\)[/tex], and the constant 19.
From this analysis, the fourth polynomial, [tex]\(23x^9 - 12x^4 + 19\)[/tex], is arranged in standard form. Therefore, the correct answer is the fourth polynomial.
Here are the given polynomials:
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
3. [tex]\(19x + 6x^2 + 2\)[/tex]
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]
Let's examine each one to check if it's in standard form:
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]: The terms arranged by degrees are [tex]\(24x^5\)[/tex], [tex]\(2x^4\)[/tex], and the constant 6. Currently, it's not in standard form because the highest degree term [tex]\(24x^5\)[/tex] is not written first.
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]: The correct order from highest to lowest degree should be [tex]\(12x^4\)[/tex], [tex]\(-9x^3\)[/tex], and [tex]\(6x^2\)[/tex]. It's not in standard form as written.
3. [tex]\(19x + 6x^2 + 2\)[/tex]: The terms arranged in standard form should have been [tex]\(6x^2\)[/tex], [tex]\(19x\)[/tex], and 2. So, this is also not in standard form as given.
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]: This polynomial is already in standard form, with the degrees in descending order: [tex]\(23x^9\)[/tex], [tex]\(-12x^4\)[/tex], and the constant 19.
From this analysis, the fourth polynomial, [tex]\(23x^9 - 12x^4 + 19\)[/tex], is arranged in standard form. Therefore, the correct answer is the fourth polynomial.
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