Answer :
To determine which polynomial is in standard form, let's review what a standard form polynomial looks like. A polynomial is in standard form when its terms are written in descending order of their degree (the exponents on the variable).
Let's analyze each option:
1. Option 1: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- In standard form, we should list the terms from highest to lowest degree. The terms here are [tex]\(24x^5\)[/tex], [tex]\(2x^4\)[/tex], and [tex]\(6\)[/tex]. After rearranging, it would be [tex]\(24x^5 + 2x^4 + 6\)[/tex].
2. Option 2: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- We arrange the terms in order of descending powers. The terms here are [tex]\(12x^4\)[/tex], [tex]\(-9x^3\)[/tex], and [tex]\(6x^2\)[/tex]. In standard form, it should be [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
3. Option 3: [tex]\(19x + 6x^2 + 2\)[/tex]
- With the terms written in descending order, you have [tex]\(6x^2\)[/tex], [tex]\(19x\)[/tex], and [tex]\(2\)[/tex]. The standard form would thus be [tex]\(6x^2 + 19x + 2\)[/tex].
4. Option 4: [tex]\(23x^8 - 12x^4 + 19\)[/tex]
- This polynomial is already in the correct order: [tex]\(23x^8\)[/tex], [tex]\(-12x^4\)[/tex], and [tex]\(19\)[/tex]. It is presented from the highest degree to the lowest (constant term).
The polynomial that is already in standard form is Option 4: [tex]\(23x^8 - 12x^4 + 19\)[/tex].
Let's analyze each option:
1. Option 1: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- In standard form, we should list the terms from highest to lowest degree. The terms here are [tex]\(24x^5\)[/tex], [tex]\(2x^4\)[/tex], and [tex]\(6\)[/tex]. After rearranging, it would be [tex]\(24x^5 + 2x^4 + 6\)[/tex].
2. Option 2: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- We arrange the terms in order of descending powers. The terms here are [tex]\(12x^4\)[/tex], [tex]\(-9x^3\)[/tex], and [tex]\(6x^2\)[/tex]. In standard form, it should be [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
3. Option 3: [tex]\(19x + 6x^2 + 2\)[/tex]
- With the terms written in descending order, you have [tex]\(6x^2\)[/tex], [tex]\(19x\)[/tex], and [tex]\(2\)[/tex]. The standard form would thus be [tex]\(6x^2 + 19x + 2\)[/tex].
4. Option 4: [tex]\(23x^8 - 12x^4 + 19\)[/tex]
- This polynomial is already in the correct order: [tex]\(23x^8\)[/tex], [tex]\(-12x^4\)[/tex], and [tex]\(19\)[/tex]. It is presented from the highest degree to the lowest (constant term).
The polynomial that is already in standard form is Option 4: [tex]\(23x^8 - 12x^4 + 19\)[/tex].
