Question

question 8 of 10
which polynomial lists the powers in descending order?

a. $3x^6 + 10x^2 + x^8 + 8x^3 - 2$

b. $x^8 + 10x^2 + 8x^3 + 3x^6 - 2$

c. $10x^2 + 8x^3 + x^8 - 2 + 3x^6$

d. $x^8 + 3x^6 + 8x^3 + 10x^2 - 2$

Explanation:

Step1: Recall descending order of powers

Descending order of powers means arranging terms from the highest exponent to the lowest exponent (and constant term at the end as it has exponent 0).

Step2: Analyze each option

• Option A: Terms are \(3x^6\) (exponent 6), \(10x^2\) (exponent 2), \(x^8\) (exponent 8), \(8x^3\) (exponent 3), \(-2\) (exponent 0). Not in descending order.
• Option B: Terms are \(x^8\) (exponent 8), \(10x^2\) (exponent 2), \(8x^3\) (exponent 3), \(3x^6\) (exponent 6), \(-2\) (exponent 0). Not in descending order.
• Option C: Terms are \(10x^2\) (exponent 2), \(8x^3\) (exponent 3), \(x^8\) (exponent 8), \(-2\) (exponent 0), \(3x^6\) (exponent 6). Not in descending order.
• Option D: Terms are \(x^8\) (exponent 8), \(3x^6\) (exponent 6), \(8x^3\) (exponent 3), \(10x^2\) (exponent 2), \(-2\) (exponent 0). This is in descending order of exponents.

Answer:

D. \( x^8 + 3x^6 + 8x^3 + 10x^2 - 2 \)