Answer :
We are given the polynomial
[tex]$$
5x^3 - x + 9x^7 + 4 + 3x^{11}.
$$[/tex]
To write it in descending order, we must list the terms starting with the highest exponent and ending with the constant term. Follow these steps:
1. Identify the exponents in each term:
- For [tex]$3x^{11}$[/tex], the exponent is [tex]$11$[/tex].
- For [tex]$9x^7$[/tex], the exponent is [tex]$7$[/tex].
- For [tex]$5x^3$[/tex], the exponent is [tex]$3$[/tex].
- For [tex]$-x$[/tex], the exponent is [tex]$1$[/tex].
- For [tex]$4$[/tex], the exponent is [tex]$0$[/tex].
2. Rearrange the terms in order of decreasing exponent:
- The term with the highest exponent is [tex]$3x^{11}$[/tex].
- Next is [tex]$9x^7$[/tex].
- Then comes [tex]$5x^3$[/tex].
- After that, [tex]$-x$[/tex] (which is [tex]$-1x^1$[/tex]).
- Finally, the constant [tex]$4$[/tex] is placed last.
3. The polynomial in descending order becomes:
[tex]$$
3x^{11} + 9x^7 + 5x^3 - x + 4.
$$[/tex]
Matching this arrangement with the given options, we see that the correct answer is option B.
[tex]$$
5x^3 - x + 9x^7 + 4 + 3x^{11}.
$$[/tex]
To write it in descending order, we must list the terms starting with the highest exponent and ending with the constant term. Follow these steps:
1. Identify the exponents in each term:
- For [tex]$3x^{11}$[/tex], the exponent is [tex]$11$[/tex].
- For [tex]$9x^7$[/tex], the exponent is [tex]$7$[/tex].
- For [tex]$5x^3$[/tex], the exponent is [tex]$3$[/tex].
- For [tex]$-x$[/tex], the exponent is [tex]$1$[/tex].
- For [tex]$4$[/tex], the exponent is [tex]$0$[/tex].
2. Rearrange the terms in order of decreasing exponent:
- The term with the highest exponent is [tex]$3x^{11}$[/tex].
- Next is [tex]$9x^7$[/tex].
- Then comes [tex]$5x^3$[/tex].
- After that, [tex]$-x$[/tex] (which is [tex]$-1x^1$[/tex]).
- Finally, the constant [tex]$4$[/tex] is placed last.
3. The polynomial in descending order becomes:
[tex]$$
3x^{11} + 9x^7 + 5x^3 - x + 4.
$$[/tex]
Matching this arrangement with the given options, we see that the correct answer is option B.
