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Answer :
To write a polynomial in descending order, we need to arrange its terms from the highest power of [tex]\( x \)[/tex] to the lowest power of [tex]\( x \)[/tex].
Given the polynomial:
[tex]\[ 2x^2 - 4x + x^6 + 8 + 3x^{10} \][/tex]
Step-by-step, we identify the powers of [tex]\( x \)[/tex] in each term:
- The term [tex]\( 2x^2 \)[/tex] has a power of 2.
- The term [tex]\( -4x \)[/tex] has a power of 1.
- The term [tex]\( x^6 \)[/tex] has a power of 6.
- The term [tex]\( 8 \)[/tex] has a power of 0 (since there is no [tex]\( x \)[/tex]).
- The term [tex]\( 3x^{10} \)[/tex] has a power of 10.
Next, we arrange these terms in descending order by their powers of [tex]\( x \)[/tex]:
- The highest power is [tex]\( 10 \)[/tex], so [tex]\( 3x^{10} \)[/tex] comes first.
- The next highest power is [tex]\( 6 \)[/tex], so [tex]\( x^6 \)[/tex] comes next.
- The next highest power is [tex]\( 2 \)[/tex], so [tex]\( 2x^2 \)[/tex] comes next.
- The next highest power is [tex]\( 1 \)[/tex], so [tex]\( -4x \)[/tex] comes next.
- The lowest power is [tex]\( 0 \)[/tex], so [tex]\( 8 \)[/tex] comes last.
So, the polynomial in descending order is:
[tex]\[ 3x^{10} + x^6 + 2x^2 - 4x + 8 \][/tex]
Among the options given, this matches option B:
B. [tex]\( 3x^{10} + x^6 + 2x^2 - 4x + 8 \)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
Given the polynomial:
[tex]\[ 2x^2 - 4x + x^6 + 8 + 3x^{10} \][/tex]
Step-by-step, we identify the powers of [tex]\( x \)[/tex] in each term:
- The term [tex]\( 2x^2 \)[/tex] has a power of 2.
- The term [tex]\( -4x \)[/tex] has a power of 1.
- The term [tex]\( x^6 \)[/tex] has a power of 6.
- The term [tex]\( 8 \)[/tex] has a power of 0 (since there is no [tex]\( x \)[/tex]).
- The term [tex]\( 3x^{10} \)[/tex] has a power of 10.
Next, we arrange these terms in descending order by their powers of [tex]\( x \)[/tex]:
- The highest power is [tex]\( 10 \)[/tex], so [tex]\( 3x^{10} \)[/tex] comes first.
- The next highest power is [tex]\( 6 \)[/tex], so [tex]\( x^6 \)[/tex] comes next.
- The next highest power is [tex]\( 2 \)[/tex], so [tex]\( 2x^2 \)[/tex] comes next.
- The next highest power is [tex]\( 1 \)[/tex], so [tex]\( -4x \)[/tex] comes next.
- The lowest power is [tex]\( 0 \)[/tex], so [tex]\( 8 \)[/tex] comes last.
So, the polynomial in descending order is:
[tex]\[ 3x^{10} + x^6 + 2x^2 - 4x + 8 \][/tex]
Among the options given, this matches option B:
B. [tex]\( 3x^{10} + x^6 + 2x^2 - 4x + 8 \)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
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