Answer :
To determine which polynomial lists the powers of [tex]\( x \)[/tex] in descending order, we need to examine each polynomial and check the sequence of the exponents.
Choice A: [tex]\( x^8+3x^6+8x^3+10x^2-2 \)[/tex]
- Powers: [tex]\( 8, 6, 3, 2, 0 \)[/tex]
- The exponents are listed in descending order.
Choice B: [tex]\( 3x^6+10x^2+x^8+8x^3-2 \)[/tex]
- Powers: [tex]\( 6, 2, 8, 3, 0 \)[/tex]
- The exponents are not in descending order.
Choice C: [tex]\( 10x^2+8x^3+x^8-2+3x^6 \)[/tex]
- Powers: [tex]\( 2, 3, 8, 0, 6 \)[/tex]
- The exponents are not in descending order.
Choice D: [tex]\( x^8+10x^2+8x^3+3x^5-2 \)[/tex]
- Powers: [tex]\( 8, 2, 3, 5, 0 \)[/tex]
- The exponents are not in descending order.
Among these choices, only Choice A lists the exponents in descending order. Therefore, the correct answer is:
Choice A: [tex]\( x^8+3x^6+8x^3+10x^2-2 \)[/tex]
Choice A: [tex]\( x^8+3x^6+8x^3+10x^2-2 \)[/tex]
- Powers: [tex]\( 8, 6, 3, 2, 0 \)[/tex]
- The exponents are listed in descending order.
Choice B: [tex]\( 3x^6+10x^2+x^8+8x^3-2 \)[/tex]
- Powers: [tex]\( 6, 2, 8, 3, 0 \)[/tex]
- The exponents are not in descending order.
Choice C: [tex]\( 10x^2+8x^3+x^8-2+3x^6 \)[/tex]
- Powers: [tex]\( 2, 3, 8, 0, 6 \)[/tex]
- The exponents are not in descending order.
Choice D: [tex]\( x^8+10x^2+8x^3+3x^5-2 \)[/tex]
- Powers: [tex]\( 8, 2, 3, 5, 0 \)[/tex]
- The exponents are not in descending order.
Among these choices, only Choice A lists the exponents in descending order. Therefore, the correct answer is:
Choice A: [tex]\( x^8+3x^6+8x^3+10x^2-2 \)[/tex]
