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When the expression [tex]\(x^4 + 7x - 3x^2 - x^3\)[/tex] is written with terms in descending order, which list represents the coefficients of the terms?

A. [tex]\(-1, 1, -3, 7\)[/tex]
B. [tex]\(1, -3, -1, 7\)[/tex]
C. [tex]\(1, -1, -3, 7\)[/tex]
D. [tex]\(1, 1, 3, 7\)[/tex]

Sagot :

GinnyAnswer
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]
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