Answer :
To write the polynomial in descending order, we need to rearrange the terms based on the exponents from the highest to the lowest. Here’s a detailed step-by-step solution:
1. Identify the Terms:
The given polynomial is [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex]. It consists of four terms: [tex]\(3x^3\)[/tex], [tex]\(9x^7\)[/tex], [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex]), and [tex]\(4x^{12}\)[/tex].
2. List the Exponents:
- For [tex]\(4x^{12}\)[/tex], the exponent is 12.
- For [tex]\(9x^7\)[/tex], the exponent is 7.
- For [tex]\(3x^3\)[/tex], the exponent is 3.
- For [tex]\(-x\)[/tex], the exponent is 1.
3. Order the Terms:
We need to order these terms by their exponents in descending order:
- The highest exponent is 12, so [tex]\(4x^{12}\)[/tex] comes first.
- The next highest exponent is 7, so [tex]\(9x^7\)[/tex] comes next.
- Then, the exponent 3, so [tex]\(3x^3\)[/tex] follows.
- Finally, the exponent 1, so [tex]\(-x\)[/tex] is last.
4. Write the Polynomial:
Arranging the terms based on the descending order of their exponents, we get:
[tex]\[
4x^{12} + 9x^7 + 3x^3 - x
\][/tex]
Therefore, the polynomial written in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex], which matches option D.
1. Identify the Terms:
The given polynomial is [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex]. It consists of four terms: [tex]\(3x^3\)[/tex], [tex]\(9x^7\)[/tex], [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex]), and [tex]\(4x^{12}\)[/tex].
2. List the Exponents:
- For [tex]\(4x^{12}\)[/tex], the exponent is 12.
- For [tex]\(9x^7\)[/tex], the exponent is 7.
- For [tex]\(3x^3\)[/tex], the exponent is 3.
- For [tex]\(-x\)[/tex], the exponent is 1.
3. Order the Terms:
We need to order these terms by their exponents in descending order:
- The highest exponent is 12, so [tex]\(4x^{12}\)[/tex] comes first.
- The next highest exponent is 7, so [tex]\(9x^7\)[/tex] comes next.
- Then, the exponent 3, so [tex]\(3x^3\)[/tex] follows.
- Finally, the exponent 1, so [tex]\(-x\)[/tex] is last.
4. Write the Polynomial:
Arranging the terms based on the descending order of their exponents, we get:
[tex]\[
4x^{12} + 9x^7 + 3x^3 - x
\][/tex]
Therefore, the polynomial written in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex], which matches option D.
