Which polynomial is written with the powers of $x$ in descending order?

• A. $3x^4+5x-2x^3-1$
• B. $5x+3x^4-1-2x^3$
• C. $3x^4-2x^3+5x-1$
• D. $\mathrm{-}1+5x-2x^3+3x^4$

Answer: (C)

Verified step by step guidance

1. Understand that a polynomial written in descending order means the terms are arranged from the highest power of \(x\) to the lowest power of \(x\).
2. Identify the powers of \(x\) in each term of the polynomial. For example, in the term \$3x^4\(, the power of \)x\( is 4; in \)-2x^3\(, the power is 3; in \)5x\(, the power is 1; and in \)-1$, the power is 0 (since it is a constant).
3. Compare the given polynomials and check the order of the powers of \(x\) in each. The correct polynomial should start with the term having the highest exponent, then the next highest, and so on, down to the constant term.
4. Rearrange the terms if necessary so that the powers of \(x\) decrease from left to right. For example, the polynomial should be ordered as \$3x^4 - 2x^3 + 5x - 1$.
5. Confirm that the polynomial you have matches the one with terms in descending order of powers of \(x\).