Answer :

To put the polynomial in descending order, we need to arrange the terms based on the exponents of [tex]\( x \)[/tex], starting from the highest exponent to the lowest. Let's break it down step by step:

1. Identify the Terms:
- The polynomial given is [tex]\(-7x^3 + 4 - 5x^9 + 9x^6 - 6x^2\)[/tex].
- The terms are: [tex]\(-5x^9\)[/tex], [tex]\(9x^6\)[/tex], [tex]\(-7x^3\)[/tex], [tex]\(-6x^2\)[/tex], and [tex]\(4\)[/tex].

2. List the Exponents:
- Notice the exponents: [tex]\(9, 6, 3, 2, \)[/tex] and for [tex]\(4\)[/tex], the exponent is [tex]\(0\)[/tex] (since [tex]\(4\)[/tex] is a constant term).

3. Arrange the Terms by Decreasing Exponents:
- The terms should be ordered starting with the highest exponent.
- Thus, the order by exponent will be: [tex]\(x^9, x^6, x^3, x^2, \text{and the constant term}\)[/tex].

4. Reorder the Polynomial:
- So, the polynomial in descending order is: [tex]\(-5x^9 + 9x^6 - 7x^3 - 6x^2 + 4\)[/tex].

Therefore, the polynomial arranged in descending order is:

[tex]\[
-5x^9 + 9x^6 - 7x^3 - 6x^2 + 4
\][/tex]

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Rewritten by : Barada