Answer :
To write a polynomial in descending order, you need to arrange the terms based on the power of [tex]\( x \)[/tex] from highest to lowest. Let's take a look at the given polynomial:
[tex]\[ 2x^2 - 4x + x^6 + 8 + 3x^{10} \][/tex]
Here are the steps to rearrange this polynomial in descending order:
1. Identify the terms:
- [tex]\( 3x^{10} \)[/tex]
- [tex]\( x^6 \)[/tex]
- [tex]\( 2x^2 \)[/tex]
- [tex]\( -4x \)[/tex]
- [tex]\( 8 \)[/tex]
2. Order by the exponents of [tex]\( x \)[/tex]:
- The term with the highest exponent is [tex]\( 3x^{10} \)[/tex].
- The next highest is [tex]\( x^6 \)[/tex].
- Followed by [tex]\( 2x^2 \)[/tex].
- Then, [tex]\( -4x \)[/tex].
- Finally, the constant term [tex]\( 8 \)[/tex].
3. Write the polynomial with terms ordered by descending exponents:
[tex]\[ 3x^{10} + x^6 + 2x^2 - 4x + 8 \][/tex]
By following these steps, you should see that the polynomial in descending order is correctly arranged as:
[tex]\[ 3x^{10} + x^6 + 2x^2 - 4x + 8 \][/tex]
Based on the options provided, the correct answer is:
C. [tex]\( 3x^{10} + x^6 + 2x^2 - 4x + 8 \)[/tex]
[tex]\[ 2x^2 - 4x + x^6 + 8 + 3x^{10} \][/tex]
Here are the steps to rearrange this polynomial in descending order:
1. Identify the terms:
- [tex]\( 3x^{10} \)[/tex]
- [tex]\( x^6 \)[/tex]
- [tex]\( 2x^2 \)[/tex]
- [tex]\( -4x \)[/tex]
- [tex]\( 8 \)[/tex]
2. Order by the exponents of [tex]\( x \)[/tex]:
- The term with the highest exponent is [tex]\( 3x^{10} \)[/tex].
- The next highest is [tex]\( x^6 \)[/tex].
- Followed by [tex]\( 2x^2 \)[/tex].
- Then, [tex]\( -4x \)[/tex].
- Finally, the constant term [tex]\( 8 \)[/tex].
3. Write the polynomial with terms ordered by descending exponents:
[tex]\[ 3x^{10} + x^6 + 2x^2 - 4x + 8 \][/tex]
By following these steps, you should see that the polynomial in descending order is correctly arranged as:
[tex]\[ 3x^{10} + x^6 + 2x^2 - 4x + 8 \][/tex]
Based on the options provided, the correct answer is:
C. [tex]\( 3x^{10} + x^6 + 2x^2 - 4x + 8 \)[/tex]
