Answer :
Sure! Let's write the polynomial in descending order of the exponents (powers) of [tex]\(x\)[/tex].
The polynomial given is:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
To arrange the terms in descending order:
1. Identify the degree of each term:
- [tex]\(4x^{12}\)[/tex] has a degree of 12.
- [tex]\(9x^7\)[/tex] has a degree of 7.
- [tex]\(3x^3\)[/tex] has a degree of 3.
- [tex]\(-x\)[/tex] is equivalent to [tex]\(-1x^1\)[/tex], with a degree of 1.
2. List the terms from highest to lowest degree:
- Start with the highest degree, which is 12: [tex]\(4x^{12}\)[/tex].
- Next, the degree is 7: [tex]\(9x^7\)[/tex].
- Then, the degree is 3: [tex]\(3x^3\)[/tex].
- Finally, the degree is 1: [tex]\(-x\)[/tex].
Putting it all together, the polynomial written in descending order is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
This matches option C. So, the correct answer is C.
The polynomial given is:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
To arrange the terms in descending order:
1. Identify the degree of each term:
- [tex]\(4x^{12}\)[/tex] has a degree of 12.
- [tex]\(9x^7\)[/tex] has a degree of 7.
- [tex]\(3x^3\)[/tex] has a degree of 3.
- [tex]\(-x\)[/tex] is equivalent to [tex]\(-1x^1\)[/tex], with a degree of 1.
2. List the terms from highest to lowest degree:
- Start with the highest degree, which is 12: [tex]\(4x^{12}\)[/tex].
- Next, the degree is 7: [tex]\(9x^7\)[/tex].
- Then, the degree is 3: [tex]\(3x^3\)[/tex].
- Finally, the degree is 1: [tex]\(-x\)[/tex].
Putting it all together, the polynomial written in descending order is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
This matches option C. So, the correct answer is C.
