Answer :
To write the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] in descending order, we'll arrange the terms based on the exponents of [tex]\(x\)[/tex], starting with the highest exponent and moving to the lowest.
Here's how you can do it:
1. Identify the Exponents: List the exponents of each term:
- [tex]\(3x^3\)[/tex] has an exponent of 3.
- [tex]\(9x^7\)[/tex] has an exponent of 7.
- [tex]\(-x\)[/tex] can be written as [tex]\(-1x^1\)[/tex] and has an exponent of 1.
- [tex]\(4x^{12}\)[/tex] has an exponent of 12.
2. Order the Exponents: Arrange these exponents in descending order: 12, 7, 3, 1.
3. Rearrange the Terms: Arrange the terms of the polynomial following the descending order of their exponents:
- The term with the highest exponent, [tex]\(4x^{12}\)[/tex], comes first.
- Next, the term [tex]\(9x^7\)[/tex].
- Then, the term [tex]\(3x^3\)[/tex].
- Finally, the term [tex]\(-x\)[/tex].
Putting it all together, the polynomial in descending order is:
[tex]\[4x^{12} + 9x^7 + 3x^3 - x\][/tex]
This matches choice B from the given options. Thus, the correct answer is:
B. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
Here's how you can do it:
1. Identify the Exponents: List the exponents of each term:
- [tex]\(3x^3\)[/tex] has an exponent of 3.
- [tex]\(9x^7\)[/tex] has an exponent of 7.
- [tex]\(-x\)[/tex] can be written as [tex]\(-1x^1\)[/tex] and has an exponent of 1.
- [tex]\(4x^{12}\)[/tex] has an exponent of 12.
2. Order the Exponents: Arrange these exponents in descending order: 12, 7, 3, 1.
3. Rearrange the Terms: Arrange the terms of the polynomial following the descending order of their exponents:
- The term with the highest exponent, [tex]\(4x^{12}\)[/tex], comes first.
- Next, the term [tex]\(9x^7\)[/tex].
- Then, the term [tex]\(3x^3\)[/tex].
- Finally, the term [tex]\(-x\)[/tex].
Putting it all together, the polynomial in descending order is:
[tex]\[4x^{12} + 9x^7 + 3x^3 - x\][/tex]
This matches choice B from the given options. Thus, the correct answer is:
B. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
