Which polynomial lists the powers in descending order? A.
B.
C.
D.
The Correct Answer and Explanation is:
The correct answer is: B.
4×5+3×4−x3−2×2+14x^5 + 3x^4 – x^3 – 2x^2 + 1
Explanation
To identify the polynomial that lists powers in descending order, we must check the exponents of xx in each term. Descending order means the exponents go from largest to smallest from left to right.
Let’s analyze the options:
- A. 4×5−2×2−x3+3×4+14x^5 – 2x^2 – x^3 + 3x^4 + 1
- Exponents appear in this sequence: 5, 2, 3, 4 → Not descending.
- B. 4×5+3×4−x3−2×2+14x^5 + 3x^4 – x^3 – 2x^2 + 1
- Exponents: 5, 4, 3, 2, 0 → Perfect descending order ✅
- C. 3×4−x3+4×5−2×2+13x^4 – x^3 + 4x^5 – 2x^2 + 1
- Exponents: 4, 3, 5, 2 → Not descending, as 5 comes after 3.
- D. 1−2×2−x3+4×5+3×41 – 2x^2 – x^3 + 4x^5 + 3x^4
- Exponents: 0, 2, 3, 5, 4 → Not descending, also disorganized.
Why B is Correct
Option B follows a clear, correct pattern:
- The first term is x5x^5 — the highest power.
- Followed by x4x^4, then x3x^3, and so on down to the constant (which is technically x0x^0).
This organization is standard in mathematics because it allows easier comparison, simplification, and operation of polynomials. When expressions are arranged in descending order, you can quickly:
- Identify the degree (the highest exponent).
- Compare polynomials.
- Perform operations like long division or factoring more efficiently.
Conclusion
Option B is the only polynomial among the choices that correctly lists terms from highest to lowest power of xx. This ordering is essential for clarity and proper mathematical formatting, especially in algebra and calculus.
✅ Correct Answer: B. 4×5+3×4−x3−2×2+14x^5 + 3x^4 – x^3 – 2x^2 + 1
