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Answer :
To arrange the terms of a polynomial in descending order, we need to order the terms by the exponent on $x$ from the highest to the lowest. The constant term can be thought of as having an exponent of zero.
Let's examine option D:
$$
x^8 + 3x^6 + 8x^3 + 10x^2 - 2.
$$
In this polynomial, the exponents are:
- The first term has $x^8$ (exponent 8).
- The second term has $3x^6$ (exponent 6).
- The third term has $8x^3$ (exponent 3).
- The fourth term has $10x^2$ (exponent 2).
- The final term is $-2$, which corresponds to $x^0$ (exponent 0).
Since the exponents $8, 6, 3, 2, 0$ are in descending order, this polynomial is correctly written with the powers in descending order.
Thus, the correct answer is:
$$
\textbf{D. } x^8 + 3x^6 + 8x^3 + 10x^2 - 2.
$$
Let's examine option D:
$$
x^8 + 3x^6 + 8x^3 + 10x^2 - 2.
$$
In this polynomial, the exponents are:
- The first term has $x^8$ (exponent 8).
- The second term has $3x^6$ (exponent 6).
- The third term has $8x^3$ (exponent 3).
- The fourth term has $10x^2$ (exponent 2).
- The final term is $-2$, which corresponds to $x^0$ (exponent 0).
Since the exponents $8, 6, 3, 2, 0$ are in descending order, this polynomial is correctly written with the powers in descending order.
Thus, the correct answer is:
$$
\textbf{D. } x^8 + 3x^6 + 8x^3 + 10x^2 - 2.
$$
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