College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Which of the following shows the polynomial below written in descending order?

[tex]\[5x^3 - x + 9x^7 + 4 + 3x^{11}\][/tex]

A. [tex]\[4 + 3x^{11} + 9x^7 + 5x^3 - x\][/tex]

B. [tex]\[3x^{11} + 9x^7 + 5x^3 - x + 4\][/tex]

C. [tex]\[9x^7 + 5x^3 + 4 + 3x^{11} - x\][/tex]

D. [tex]\[3x^{11} + 9x^7 - x + 4 + 5x^3\][/tex]

Answer :

To arrange a polynomial in descending order, we need to order all the terms from the highest to the lowest exponent of [tex]\( x \)[/tex]. Let's look at the polynomial given:

[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]

Here are the steps to ordering it:

1. Identify the exponents of each term:
- [tex]\( 3x^{11} \)[/tex] has the highest exponent, which is 11.
- [tex]\( 9x^7 \)[/tex] has an exponent of 7.
- [tex]\( 5x^3 \)[/tex] has an exponent of 3.
- [tex]\( -x \)[/tex] can be rewritten as [tex]\(-1x^1\)[/tex] and has an exponent of 1.
- The constant term [tex]\( 4 \)[/tex] can be considered as [tex]\( 4x^0 \)[/tex] with an exponent of 0.

2. Reorder the terms from highest to lowest exponent:
- Start with the term with the highest exponent: [tex]\( 3x^{11} \)[/tex].
- Next is the term with the next highest exponent: [tex]\( 9x^7 \)[/tex].
- Followed by: [tex]\( 5x^3 \)[/tex].
- Then: [tex]\(-x\)[/tex].
- Finally, the constant term: [tex]\( 4 \)[/tex].

3. Write the polynomial in descending order:
- Combine all these ordered terms to get:

[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]

Thus, the polynomial written in descending order is:

[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]

So, the correct answer is option B:

[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]