To write the given polynomial in descending order of exponents, we need to look at the exponents of [tex]\( x \)[/tex] in each term and arrange the terms from highest to lowest exponent.
The polynomial provided is:
[tex]\[ 5x^3 - x + 9x^7 + 4 + 3x^{11} \][/tex]
Let's identify each term and its exponent:
- [tex]\( 3x^{11} \)[/tex]: exponent 11
- [tex]\( 9x^7 \)[/tex]: exponent 7
- [tex]\( 5x^3 \)[/tex]: exponent 3
- [tex]\( -x \)[/tex]: exponent 1 (since it's [tex]\( -1x^1 \)[/tex])
- [tex]\( 4 \)[/tex]: exponent 0
Now, we'll list these terms from highest to lowest exponent:
1. [tex]\( 3x^{11} \)[/tex] (exponent 11)
2. [tex]\( 9x^7 \)[/tex] (exponent 7)
3. [tex]\( 5x^3 \)[/tex] (exponent 3)
4. [tex]\( -x \)[/tex] (exponent 1)
5. [tex]\( 4 \)[/tex] (exponent 0)
So, the polynomial in descending order is:
[tex]\[ 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
Now let's verify which option matches this order:
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]
The correct option is:
[tex]\[ \text{B. } 3x^{11} + 9x^7 + 5x^3 - x + 4 \][/tex]
