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Answer :
To write a polynomial in descending order, you need to arrange its terms starting with the highest power of [tex]\(x\)[/tex] and go down to the lowest power. Let's do this with the given polynomial: [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex].
Here are the steps:
1. Identify the terms and their exponents:
- The term [tex]\(3x^3\)[/tex] has an exponent of 3.
- The term [tex]\(9x^7\)[/tex] has an exponent of 7.
- The term [tex]\(-x\)[/tex] can be thought of as [tex]\(-1x^1\)[/tex] since it has an exponent of 1.
- The term [tex]\(4x^{12}\)[/tex] has an exponent of 12.
2. List the terms with their exponents:
- [tex]\(4x^{12}\)[/tex]
- [tex]\(9x^7\)[/tex]
- [tex]\(3x^3\)[/tex]
- [tex]\(-x\)[/tex]
3. Arrange the terms by decreasing order of the exponents:
- Start with the highest exponent, which is 12, and use the term [tex]\(4x^{12}\)[/tex].
- The next highest exponent is 7, so use the term [tex]\(9x^7\)[/tex].
- Next, we have the exponent 3, so use the term [tex]\(3x^3\)[/tex].
- Lastly, the lowest exponent is 1, and the term is [tex]\(-x\)[/tex].
4. Write the polynomial with the terms in the correct order:
- The polynomial in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
Therefore, the polynomial written in descending order is:
[tex]\[ \boxed{4x^{12} + 9x^7 + 3x^3 - x} \][/tex]
The correct option is A.
Here are the steps:
1. Identify the terms and their exponents:
- The term [tex]\(3x^3\)[/tex] has an exponent of 3.
- The term [tex]\(9x^7\)[/tex] has an exponent of 7.
- The term [tex]\(-x\)[/tex] can be thought of as [tex]\(-1x^1\)[/tex] since it has an exponent of 1.
- The term [tex]\(4x^{12}\)[/tex] has an exponent of 12.
2. List the terms with their exponents:
- [tex]\(4x^{12}\)[/tex]
- [tex]\(9x^7\)[/tex]
- [tex]\(3x^3\)[/tex]
- [tex]\(-x\)[/tex]
3. Arrange the terms by decreasing order of the exponents:
- Start with the highest exponent, which is 12, and use the term [tex]\(4x^{12}\)[/tex].
- The next highest exponent is 7, so use the term [tex]\(9x^7\)[/tex].
- Next, we have the exponent 3, so use the term [tex]\(3x^3\)[/tex].
- Lastly, the lowest exponent is 1, and the term is [tex]\(-x\)[/tex].
4. Write the polynomial with the terms in the correct order:
- The polynomial in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
Therefore, the polynomial written in descending order is:
[tex]\[ \boxed{4x^{12} + 9x^7 + 3x^3 - x} \][/tex]
The correct option is A.
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