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Answer :
To determine which polynomial lists the powers in descending order, we need to analyze each option and arrange the terms from the highest power of [tex]\( x \)[/tex] to the lowest.
Let's look at the options:
A. [tex]\( 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
- Examine the powers: 6, 2, 8, 3, and 0 (constant term has no [tex]\( x \)[/tex] power).
- This is not in descending order as the term [tex]\( x^8 \)[/tex] should be first.
B. [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
- Examine the powers: 8, 6, 3, 2, and 0.
- The powers are in descending order from highest to lowest.
C. [tex]\( x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
- Examine the powers: 8, 2, 3, 6, and 0.
- The powers are not in descending order.
D. [tex]\( 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \)[/tex]
- Examine the powers: 2, 3, 8, 0, and 6.
- The powers are not in descending order.
The correct polynomial, where the powers of [tex]\( x \)[/tex] are listed from highest to lowest, is:
B. [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
This sequence is [tex]\[ 8, 6, 3, 2, 0 \][/tex], which is in strict descending order.
Let's look at the options:
A. [tex]\( 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
- Examine the powers: 6, 2, 8, 3, and 0 (constant term has no [tex]\( x \)[/tex] power).
- This is not in descending order as the term [tex]\( x^8 \)[/tex] should be first.
B. [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
- Examine the powers: 8, 6, 3, 2, and 0.
- The powers are in descending order from highest to lowest.
C. [tex]\( x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
- Examine the powers: 8, 2, 3, 6, and 0.
- The powers are not in descending order.
D. [tex]\( 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \)[/tex]
- Examine the powers: 2, 3, 8, 0, and 6.
- The powers are not in descending order.
The correct polynomial, where the powers of [tex]\( x \)[/tex] are listed from highest to lowest, is:
B. [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
This sequence is [tex]\[ 8, 6, 3, 2, 0 \][/tex], which is in strict descending order.
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