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Answer :
To determine which polynomial lists the powers in descending order, we need to organize the terms from the highest power of [tex]\( x \)[/tex] to the lowest power.
Let's look at each option individually:
Option A: [tex]\( x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
- Powers of [tex]\( x \)[/tex]: [tex]\( 8, 2, 3, 6, 0 \)[/tex]
- In order: [tex]\( x^8, 3x^6, 8x^3, 10x^2, -2 \)[/tex]
Option B: [tex]\( 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
- Powers of [tex]\( x \)[/tex]: [tex]\( 6, 2, 8, 3, 0 \)[/tex]
- In order: [tex]\( x^8, 3x^6, 8x^3, 10x^2, -2 \)[/tex]
Option C: [tex]\( 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \)[/tex]
- Powers of [tex]\( x \)[/tex]: [tex]\( 2, 3, 8, 0, 6 \)[/tex]
- In order: [tex]\( x^8, 3x^6, 8x^3, 10x^2, -2 \)[/tex]
Option D: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
- Powers of [tex]\( x \)[/tex]: [tex]\( 8, 6, 3, 2, 0 \)[/tex]
- Already in order: [tex]\( x^8, 3x^6, 8x^3, 10x^2, -2 \)[/tex]
Option D lists the terms in descending order of the powers: [tex]\( x^8, x^6, x^3, x^2, \)[/tex] and the constant term [tex]\(-2\)[/tex]. Therefore, the correct answer is D.
Let's look at each option individually:
Option A: [tex]\( x^8 + 10x^2 + 8x^3 + 3x^6 - 2 \)[/tex]
- Powers of [tex]\( x \)[/tex]: [tex]\( 8, 2, 3, 6, 0 \)[/tex]
- In order: [tex]\( x^8, 3x^6, 8x^3, 10x^2, -2 \)[/tex]
Option B: [tex]\( 3x^6 + 10x^2 + x^8 + 8x^3 - 2 \)[/tex]
- Powers of [tex]\( x \)[/tex]: [tex]\( 6, 2, 8, 3, 0 \)[/tex]
- In order: [tex]\( x^8, 3x^6, 8x^3, 10x^2, -2 \)[/tex]
Option C: [tex]\( 10x^2 + 8x^3 + x^8 - 2 + 3x^6 \)[/tex]
- Powers of [tex]\( x \)[/tex]: [tex]\( 2, 3, 8, 0, 6 \)[/tex]
- In order: [tex]\( x^8, 3x^6, 8x^3, 10x^2, -2 \)[/tex]
Option D: [tex]\( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)[/tex]
- Powers of [tex]\( x \)[/tex]: [tex]\( 8, 6, 3, 2, 0 \)[/tex]
- Already in order: [tex]\( x^8, 3x^6, 8x^3, 10x^2, -2 \)[/tex]
Option D lists the terms in descending order of the powers: [tex]\( x^8, x^6, x^3, x^2, \)[/tex] and the constant term [tex]\(-2\)[/tex]. Therefore, the correct answer is D.
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