Answer :
To determine which polynomial is in standard form, we need to arrange the terms of each polynomial in descending order based on the degree of the terms. The standard form of a polynomial is when the terms are listed from the highest degree to the lowest.
Let's analyze the given polynomials one by one:
1. Polynomial 1: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- The degrees are: 5 for [tex]\(24x^5\)[/tex], 4 for [tex]\(2x^4\)[/tex], and 0 for the constant term 6.
- In standard form, it should be: [tex]\(24x^5 + 2x^4 + 6\)[/tex]
2. Polynomial 2: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- The degrees are: 4 for [tex]\(12x^4\)[/tex], 3 for [tex]\(-9x^3\)[/tex], and 2 for [tex]\(6x^2\)[/tex].
- In standard form, it should be: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex]
3. Polynomial 3: [tex]\(19x + 6x^2 + 2\)[/tex]
- The degrees are: 2 for [tex]\(6x^2\)[/tex], 1 for [tex]\(19x\)[/tex], and 0 for the constant term 2.
- In standard form, it should be: [tex]\(6x^2 + 19x + 2\)[/tex]
4. Polynomial 4: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- The degrees are: 9 for [tex]\(23x^9\)[/tex], 4 for [tex]\(-12x^4\)[/tex], and 0 for the constant term 19.
- This polynomial is already in standard form: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
After examining all the polynomials, we see that Polynomial 4 is already in standard form because its terms are arranged in descending order based on their degrees. Therefore, Polynomial 4 is the correct answer.
Let's analyze the given polynomials one by one:
1. Polynomial 1: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- The degrees are: 5 for [tex]\(24x^5\)[/tex], 4 for [tex]\(2x^4\)[/tex], and 0 for the constant term 6.
- In standard form, it should be: [tex]\(24x^5 + 2x^4 + 6\)[/tex]
2. Polynomial 2: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- The degrees are: 4 for [tex]\(12x^4\)[/tex], 3 for [tex]\(-9x^3\)[/tex], and 2 for [tex]\(6x^2\)[/tex].
- In standard form, it should be: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex]
3. Polynomial 3: [tex]\(19x + 6x^2 + 2\)[/tex]
- The degrees are: 2 for [tex]\(6x^2\)[/tex], 1 for [tex]\(19x\)[/tex], and 0 for the constant term 2.
- In standard form, it should be: [tex]\(6x^2 + 19x + 2\)[/tex]
4. Polynomial 4: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- The degrees are: 9 for [tex]\(23x^9\)[/tex], 4 for [tex]\(-12x^4\)[/tex], and 0 for the constant term 19.
- This polynomial is already in standard form: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
After examining all the polynomials, we see that Polynomial 4 is already in standard form because its terms are arranged in descending order based on their degrees. Therefore, Polynomial 4 is the correct answer.
