Answer:
The option D contains the powers in descending order.
Step-by-step explanation:
Descending order means that any term of the expression must have a lower order than the previous term. Keep in mind that if there is a constant (number without the [tex]x[/tex]) is because the number has implicitly the factor [tex]x^0[/tex]. However, this factor equals 1. For a better understanding, let's put the factor [tex]x^0[/tex] with the constant numbers. Now, let's analyse each option:
A. [tex]3x^6+10x^2+x^8+8x^3-2x^0[/tex]
- As the first term has a power of 6, the second term must have a lower power than 6. As it is 2, the second term is correct.
- As the second term has a power of 2, the third term must have a lower power than 2. As it is 8 (it is higher), the third term is incorrect. So, the option A is INCORRECT.
B. [tex]10x^2+8x^3+x^8-2x^0+3x^6[/tex]
- As the first term has a power of 2, the second term must have a lower power than 2. As it is 3 (it is higher), the second term is incorrect. So, the option B is INCORRECT.
C. [tex]x^8+10x^2+8x^3+3x^6-2x^0[/tex]
- As the first term has a power of 8, the second term must have a lower power than 8. As it is 2, the second term is correct.
- As the second term has a power of 2, the third term must have a lower power than 2. As it is 3 (it is higher), the third term is incorrect. So, the option C is INCORRECT.
D. [tex]x^8+3x^6+8x^3+10x^2-2x^0[/tex]
- As the first term has a power of 8, the second term must have a lower power than 8. As it is 6, the second term is correct.
- As the second term has a power of 6, the third term must have a lower power than 6. As it is 3, the third term is correct.
- As the third term has a power of 3, the fourth term must have a lower power than 3. As it is 2, the fourth term is correct.
- Finally, as the fourth term has a power of 2, the last term must have a lower power than 2. As it is 0, the last term is correct.
- As all terms are correct, the option D is the CORRECT one.
Thus, the option D contains the powers in descending order.
