Answer :
To determine which polynomial is in standard form, we need to remember that a polynomial in standard form orders the terms by descending powers of the variable [tex]\(x\)[/tex]. Let's analyze each option:
1. Option 1: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- In this expression, the terms are not in descending order. The term with the highest power of [tex]\(x\)[/tex] is [tex]\(24x^5\)[/tex], so the correct order should be [tex]\(24x^5 + 2x^4 + 6\)[/tex]. Therefore, this polynomial is not in standard form.
2. Option 2: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Here, the terms should be rearranged. The highest degree term is [tex]\(12x^4\)[/tex], so in descending order the polynomial should be written as [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex]. This polynomial is not in standard form as given.
3. Option 3: [tex]\(19x + 6x^2 + 2\)[/tex]
- The correct arrangement in descending order is [tex]\(6x^2 + 19x + 2\)[/tex]. Therefore, this polynomial is not in standard form as presented.
4. Option 4: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- This polynomial is correctly in descending order with respect to the powers of [tex]\(x\)[/tex]: [tex]\(23x^9\)[/tex], [tex]\(-12x^4\)[/tex], and the constant [tex]\(19\)[/tex].
Based on this analysis, the polynomial in standard form is:
[tex]\(23x^9 - 12x^4 + 19\)[/tex].
1. Option 1: [tex]\(2x^4 + 6 + 24x^5\)[/tex]
- In this expression, the terms are not in descending order. The term with the highest power of [tex]\(x\)[/tex] is [tex]\(24x^5\)[/tex], so the correct order should be [tex]\(24x^5 + 2x^4 + 6\)[/tex]. Therefore, this polynomial is not in standard form.
2. Option 2: [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]
- Here, the terms should be rearranged. The highest degree term is [tex]\(12x^4\)[/tex], so in descending order the polynomial should be written as [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex]. This polynomial is not in standard form as given.
3. Option 3: [tex]\(19x + 6x^2 + 2\)[/tex]
- The correct arrangement in descending order is [tex]\(6x^2 + 19x + 2\)[/tex]. Therefore, this polynomial is not in standard form as presented.
4. Option 4: [tex]\(23x^9 - 12x^4 + 19\)[/tex]
- This polynomial is correctly in descending order with respect to the powers of [tex]\(x\)[/tex]: [tex]\(23x^9\)[/tex], [tex]\(-12x^4\)[/tex], and the constant [tex]\(19\)[/tex].
Based on this analysis, the polynomial in standard form is:
[tex]\(23x^9 - 12x^4 + 19\)[/tex].
