To determine the coefficients of the polynomial when the terms are arranged in descending order, follow these steps:
1. Identify the polynomial expression:
[tex]\[
x^4 + 7x - 3x^2 - x^3
\][/tex]
2. Rewrite the polynomial with terms in descending order of powers of [tex]\( x \)[/tex]:
[tex]\[
x^4 - x^3 - 3x^2 + 7x
\][/tex]
Here, we have arranged the terms from the highest power ([tex]\( x^4 \)[/tex]) to the lowest power ([tex]\( x \)[/tex]).
3. Extract the coefficients of each term:
- For [tex]\( x^4 \)[/tex], the coefficient is [tex]\( 1 \)[/tex].
- For [tex]\( -x^3 \)[/tex], the coefficient is [tex]\( -1 \)[/tex].
- For [tex]\( -3x^2 \)[/tex], the coefficient is [tex]\( -3 \)[/tex].
- For [tex]\( 7x \)[/tex], the coefficient is [tex]\( 7 \)[/tex].
Hence, the list of coefficients in order is:
[tex]\[
[1, -1, -3, 7]
\][/tex]
So, the correct answer is:
C. [tex]\( 1, -1, -3, 7 \)[/tex]
