Answer :
To solve this problem, we need to arrange the terms of the polynomial in descending order of their exponents. Here's how we can do this:
The given polynomial is:
[tex]\[ 4x^2 - x + 8x^6 + 3 + 2x^{10} \][/tex]
To write it in descending order, we follow these steps:
1. Identify the terms and their exponents:
- [tex]\( 2x^{10} \)[/tex] has an exponent of 10.
- [tex]\( 8x^6 \)[/tex] has an exponent of 6.
- [tex]\( 4x^2 \)[/tex] has an exponent of 2.
- [tex]\(-x\)[/tex] is [tex]\( -1x^1 \)[/tex] and has an exponent of 1.
- The constant term [tex]\(3\)[/tex] has an exponent of 0.
2. Order the terms by decreasing exponents:
- Highest exponent: [tex]\( 2x^{10} \)[/tex]
- Next: [tex]\( 8x^6 \)[/tex]
- Then: [tex]\( 4x^2 \)[/tex]
- Next: [tex]\(-x\)[/tex]
- Finally: [tex]\( 3 \)[/tex]
3. Write the polynomial with the terms in order:
- Place each term in order from highest to lowest exponent:
[tex]\[ 2x^{10} + 8x^6 + 4x^2 - x + 3 \][/tex]
Now, compare this ordered polynomial with the given options:
A. [tex]\( 8x^6 + 4x^2 + 3 + 2x^{10} - x \)[/tex]
B. [tex]\( 2x^{10} + 4x^2 - x + 3 + 8x^6 \)[/tex]
C. [tex]\( 3 + 2x^{10} + 8x^6 + 4x^2 - x \)[/tex]
D. [tex]\( 2x^{10} + 8x^6 + 4x^2 - x + 3 \)[/tex]
The correct option that matches the ordered polynomial is D:
[tex]\( 2x^{10} + 8x^6 + 4x^2 - x + 3 \)[/tex]
The given polynomial is:
[tex]\[ 4x^2 - x + 8x^6 + 3 + 2x^{10} \][/tex]
To write it in descending order, we follow these steps:
1. Identify the terms and their exponents:
- [tex]\( 2x^{10} \)[/tex] has an exponent of 10.
- [tex]\( 8x^6 \)[/tex] has an exponent of 6.
- [tex]\( 4x^2 \)[/tex] has an exponent of 2.
- [tex]\(-x\)[/tex] is [tex]\( -1x^1 \)[/tex] and has an exponent of 1.
- The constant term [tex]\(3\)[/tex] has an exponent of 0.
2. Order the terms by decreasing exponents:
- Highest exponent: [tex]\( 2x^{10} \)[/tex]
- Next: [tex]\( 8x^6 \)[/tex]
- Then: [tex]\( 4x^2 \)[/tex]
- Next: [tex]\(-x\)[/tex]
- Finally: [tex]\( 3 \)[/tex]
3. Write the polynomial with the terms in order:
- Place each term in order from highest to lowest exponent:
[tex]\[ 2x^{10} + 8x^6 + 4x^2 - x + 3 \][/tex]
Now, compare this ordered polynomial with the given options:
A. [tex]\( 8x^6 + 4x^2 + 3 + 2x^{10} - x \)[/tex]
B. [tex]\( 2x^{10} + 4x^2 - x + 3 + 8x^6 \)[/tex]
C. [tex]\( 3 + 2x^{10} + 8x^6 + 4x^2 - x \)[/tex]
D. [tex]\( 2x^{10} + 8x^6 + 4x^2 - x + 3 \)[/tex]
The correct option that matches the ordered polynomial is D:
[tex]\( 2x^{10} + 8x^6 + 4x^2 - x + 3 \)[/tex]
