Question

Which polynomial contains the powers in descending order?

A. 3x6 + 10x2 + x8 + 8x3 - 2
B. 10x2 + 8x3 + x8 - 2 + 3x6
C. x8 + 10x2 + 8x3 + 3x6 - 2
D. x8 + 3x6 + 8x3 + 10x2 - 2

Answer 1

D. x⁸ + 3x⁶ + 8x³ + 10x² - 2

Answer 2

The option D contains the powers in descending order.

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
`x`) is because the number has implicitly the factor
`x^0`. However, this factor equals 1. For a better understanding, let's put the factor
`x^0` with the constant numbers. Now, let's analyse each option:

A.
`3x^6+10x^2+x^8+8x^3-2x^0`

• 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.
`10x^2+8x^3+x^8-2x^0+3x^6`

• 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.
`x^8+10x^2+8x^3+3x^6-2x^0`

• 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.
`x^8+3x^6+8x^3+10x^2-2x^0`

• 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.