Answer :
To arrange the polynomial in descending order, you need to organize the terms based on the powers of [tex]\( x \)[/tex], from the highest to the lowest. Let's go through the given polynomial:
Original polynomial: [tex]\(-4x^6 + 3x^2 - 9x^9 + 9x^7 - 9x^3\)[/tex].
1. Identify the exponents: Look at each term and identify the powers of [tex]\( x \)[/tex]:
- The term [tex]\(-9x^9\)[/tex] has the highest exponent, which is 9.
- Next is [tex]\(9x^7\)[/tex], with an exponent of 7.
- Then, [tex]\(-4x^6\)[/tex] with an exponent of 6.
- After that, [tex]\(-9x^3\)[/tex] with an exponent of 3.
- Finally, [tex]\(3x^2\)[/tex] has the smallest exponent of 2.
2. Reorder the terms: Arrange these terms by decreasing powers of [tex]\( x \)[/tex]:
- Start with the term with the highest power: [tex]\(-9x^9\)[/tex].
- Follow with the next highest: [tex]\(9x^7\)[/tex].
- Then [tex]\(-4x^6\)[/tex].
- Next, include [tex]\(-9x^3\)[/tex].
- Finally, add [tex]\(3x^2\)[/tex].
So, the polynomial in descending order is:
[tex]\[
-9x^9 + 9x^7 - 4x^6 - 9x^3 + 3x^2
\][/tex]
This organizes the polynomial from the highest degree to the lowest, making it easier to understand and work with further if needed.
Original polynomial: [tex]\(-4x^6 + 3x^2 - 9x^9 + 9x^7 - 9x^3\)[/tex].
1. Identify the exponents: Look at each term and identify the powers of [tex]\( x \)[/tex]:
- The term [tex]\(-9x^9\)[/tex] has the highest exponent, which is 9.
- Next is [tex]\(9x^7\)[/tex], with an exponent of 7.
- Then, [tex]\(-4x^6\)[/tex] with an exponent of 6.
- After that, [tex]\(-9x^3\)[/tex] with an exponent of 3.
- Finally, [tex]\(3x^2\)[/tex] has the smallest exponent of 2.
2. Reorder the terms: Arrange these terms by decreasing powers of [tex]\( x \)[/tex]:
- Start with the term with the highest power: [tex]\(-9x^9\)[/tex].
- Follow with the next highest: [tex]\(9x^7\)[/tex].
- Then [tex]\(-4x^6\)[/tex].
- Next, include [tex]\(-9x^3\)[/tex].
- Finally, add [tex]\(3x^2\)[/tex].
So, the polynomial in descending order is:
[tex]\[
-9x^9 + 9x^7 - 4x^6 - 9x^3 + 3x^2
\][/tex]
This organizes the polynomial from the highest degree to the lowest, making it easier to understand and work with further if needed.
