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Answer :
To write the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] in descending order, we need to arrange the terms based on the exponents of [tex]\(x\)[/tex] from highest to lowest. Here's how we can do that step-by-step:
1. Identify the exponents of each term:
- The term [tex]\(4x^{12}\)[/tex] has an exponent of 12.
- The term [tex]\(9x^7\)[/tex] has an exponent of 7.
- The term [tex]\(3x^3\)[/tex] has an exponent of 3.
- The term [tex]\(-x\)[/tex] is the same as [tex]\(-1x^1\)[/tex] and has an exponent of 1.
2. Order the terms based on 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 follows with the term [tex]\(3x^3\)[/tex].
- Finally, the lowest exponent is 1 for the term [tex]\(-x\)[/tex].
3. Write the polynomial with terms in descending order:
- Place the terms in the order we've identified: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
So, the correct arrangement of the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] in descending order is:
[tex]\[4x^{12} + 9x^7 + 3x^3 - x\][/tex]
Thus, the answer is option A:
[tex]\[4x^{12} + 9x^7 + 3x^3 - x\][/tex]
1. Identify the exponents of each term:
- The term [tex]\(4x^{12}\)[/tex] has an exponent of 12.
- The term [tex]\(9x^7\)[/tex] has an exponent of 7.
- The term [tex]\(3x^3\)[/tex] has an exponent of 3.
- The term [tex]\(-x\)[/tex] is the same as [tex]\(-1x^1\)[/tex] and has an exponent of 1.
2. Order the terms based on 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 follows with the term [tex]\(3x^3\)[/tex].
- Finally, the lowest exponent is 1 for the term [tex]\(-x\)[/tex].
3. Write the polynomial with terms in descending order:
- Place the terms in the order we've identified: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
So, the correct arrangement of the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] in descending order is:
[tex]\[4x^{12} + 9x^7 + 3x^3 - x\][/tex]
Thus, the answer is option A:
[tex]\[4x^{12} + 9x^7 + 3x^3 - x\][/tex]
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