Answer :
To determine which polynomial is listed with powers in descending order, we need to arrange the terms by the exponents of [tex]\(x\)[/tex], starting from the highest to the lowest power.
Let's look at each option:
A. [tex]\(3x^6 + 10x^2 + x^8 + 8x^3 - 2\)[/tex]
- Here, the term with the highest power is [tex]\(x^8\)[/tex], but it doesn't appear first.
B. [tex]\(10x^2 + 8x^3 + x^8 - 2 + 3x^6\)[/tex]
- Again, the term with the highest power, [tex]\(x^8\)[/tex], isn't listed first.
C. [tex]\(x^8 + 10x^2 + 8x^3 + 3x^6 - 2\)[/tex]
- In this case, the highest power, [tex]\(x^8\)[/tex], is first, but the subsequent terms are not in descending order.
D. [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex]
- This polynomial starts with the highest power, [tex]\(x^8\)[/tex], followed by [tex]\(x^6\)[/tex], [tex]\(x^3\)[/tex], [tex]\(x^2\)[/tex], and a constant term. The powers are in perfect descending order.
Thus, the correct answer is D. [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex] because it lists the powers of [tex]\(x\)[/tex] in descending order.
Let's look at each option:
A. [tex]\(3x^6 + 10x^2 + x^8 + 8x^3 - 2\)[/tex]
- Here, the term with the highest power is [tex]\(x^8\)[/tex], but it doesn't appear first.
B. [tex]\(10x^2 + 8x^3 + x^8 - 2 + 3x^6\)[/tex]
- Again, the term with the highest power, [tex]\(x^8\)[/tex], isn't listed first.
C. [tex]\(x^8 + 10x^2 + 8x^3 + 3x^6 - 2\)[/tex]
- In this case, the highest power, [tex]\(x^8\)[/tex], is first, but the subsequent terms are not in descending order.
D. [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex]
- This polynomial starts with the highest power, [tex]\(x^8\)[/tex], followed by [tex]\(x^6\)[/tex], [tex]\(x^3\)[/tex], [tex]\(x^2\)[/tex], and a constant term. The powers are in perfect descending order.
Thus, the correct answer is D. [tex]\(x^8 + 3x^6 + 8x^3 + 10x^2 - 2\)[/tex] because it lists the powers of [tex]\(x\)[/tex] in descending order.
