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Answer :
To determine which polynomial is in standard form, we need to know that a polynomial in standard form has its terms written in descending order of their exponents. Let's analyze each polynomial:
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]:
- The exponents here are 4 for [tex]\(x^4\)[/tex], 0 for the constant 6, and 5 for [tex]\(x^5\)[/tex].
- To be in standard form, the terms should be ordered from highest exponent to lowest: [tex]\(24x^5 + 2x^4 + 6\)[/tex].
- This polynomial is not in standard form.
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]:
- The exponents are 2 for [tex]\(x^2\)[/tex], 3 for [tex]\(x^3\)[/tex], and 4 for [tex]\(x^4\)[/tex].
- Correct order in standard form: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
- This polynomial is not in standard form.
3. [tex]\(19x + 6x^2 + 2\)[/tex]:
- The exponents are 1 for [tex]\(x\)[/tex], 2 for [tex]\(x^2\)[/tex], and 0 for the constant 2.
- Correct order in standard form: [tex]\(6x^2 + 19x + 2\)[/tex].
- This polynomial is not in standard form.
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]:
- The exponents are 9 for [tex]\(x^9\)[/tex], 4 for [tex]\(x^4\)[/tex], and 0 for the constant 19.
- This is already in the correct order of decreasing exponents: [tex]\(23x^9 - 12x^4 + 19\)[/tex].
- This polynomial is in standard form.
Therefore, the polynomial that is in standard form is [tex]\(23x^9 - 12x^4 + 19\)[/tex].
1. [tex]\(2x^4 + 6 + 24x^5\)[/tex]:
- The exponents here are 4 for [tex]\(x^4\)[/tex], 0 for the constant 6, and 5 for [tex]\(x^5\)[/tex].
- To be in standard form, the terms should be ordered from highest exponent to lowest: [tex]\(24x^5 + 2x^4 + 6\)[/tex].
- This polynomial is not in standard form.
2. [tex]\(6x^2 - 9x^3 + 12x^4\)[/tex]:
- The exponents are 2 for [tex]\(x^2\)[/tex], 3 for [tex]\(x^3\)[/tex], and 4 for [tex]\(x^4\)[/tex].
- Correct order in standard form: [tex]\(12x^4 - 9x^3 + 6x^2\)[/tex].
- This polynomial is not in standard form.
3. [tex]\(19x + 6x^2 + 2\)[/tex]:
- The exponents are 1 for [tex]\(x\)[/tex], 2 for [tex]\(x^2\)[/tex], and 0 for the constant 2.
- Correct order in standard form: [tex]\(6x^2 + 19x + 2\)[/tex].
- This polynomial is not in standard form.
4. [tex]\(23x^9 - 12x^4 + 19\)[/tex]:
- The exponents are 9 for [tex]\(x^9\)[/tex], 4 for [tex]\(x^4\)[/tex], and 0 for the constant 19.
- This is already in the correct order of decreasing exponents: [tex]\(23x^9 - 12x^4 + 19\)[/tex].
- This polynomial is in standard form.
Therefore, the polynomial that is in standard form is [tex]\(23x^9 - 12x^4 + 19\)[/tex].
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