Answer :
To arrange the polynomial [tex]\(5x^3 - x + 9x^7 + 4 + 3x^{11}\)[/tex] in descending order, we need to order the terms from the highest power of [tex]\(x\)[/tex] to the lowest. Let's break it down step by step:
1. Identify the terms and their exponents:
- [tex]\( 3x^{11} \)[/tex] (highest power is 11)
- [tex]\( 9x^7 \)[/tex] (power is 7)
- [tex]\( 5x^3 \)[/tex] (power is 3)
- [tex]\( -x \)[/tex] (which is the same as [tex]\(-1x^1\)[/tex], power is 1)
- [tex]\( 4 \)[/tex] (constant term, power is 0)
2. Order the terms from highest to lowest exponent:
- [tex]\( 3x^{11} \)[/tex]: highest degree term
- [tex]\( 9x^7 \)[/tex]
- [tex]\( 5x^3 \)[/tex]
- [tex]\( -x \)[/tex]
- [tex]\( 4 \)[/tex]: the constant term, lowest power
3. Write the polynomial with the terms in the correct order:
- The polynomial written in descending order is [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex].
By following these steps, we reordered the polynomial correctly. Therefore, the answer that reflects this order is:
C. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
1. Identify the terms and their exponents:
- [tex]\( 3x^{11} \)[/tex] (highest power is 11)
- [tex]\( 9x^7 \)[/tex] (power is 7)
- [tex]\( 5x^3 \)[/tex] (power is 3)
- [tex]\( -x \)[/tex] (which is the same as [tex]\(-1x^1\)[/tex], power is 1)
- [tex]\( 4 \)[/tex] (constant term, power is 0)
2. Order the terms from highest to lowest exponent:
- [tex]\( 3x^{11} \)[/tex]: highest degree term
- [tex]\( 9x^7 \)[/tex]
- [tex]\( 5x^3 \)[/tex]
- [tex]\( -x \)[/tex]
- [tex]\( 4 \)[/tex]: the constant term, lowest power
3. Write the polynomial with the terms in the correct order:
- The polynomial written in descending order is [tex]\( 3x^{11} + 9x^7 + 5x^3 - x + 4 \)[/tex].
By following these steps, we reordered the polynomial correctly. Therefore, the answer that reflects this order is:
C. [tex]\(3x^{11} + 9x^7 + 5x^3 - x + 4\)[/tex]
