Answer :
To write the polynomial in descending order, we need to arrange the terms by the degree of each term's exponent, starting from the highest to the lowest. Let's look at the polynomial you provided:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
Here are the steps to write this polynomial in descending order:
1. Identify the exponents in each term:
- [tex]\( 4x^{12} \)[/tex] has an exponent of 12.
- [tex]\( 9x^7 \)[/tex] has an exponent of 7.
- [tex]\( 3x^3 \)[/tex] has an exponent of 3.
- [tex]\(-x\)[/tex] can be considered as [tex]\(-1x^1\)[/tex] with an exponent of 1.
2. Order the terms by their exponents from highest to lowest:
- The highest exponent is 12, then 7, followed by 3, and finally 1.
3. Arrange the terms based on the order identified:
- The term with the exponent of 12 is [tex]\( 4x^{12} \)[/tex].
- The term with the exponent of 7 is [tex]\( 9x^7 \)[/tex].
- The term with the exponent of 3 is [tex]\( 3x^3 \)[/tex].
- The term with the exponent of 1 is [tex]\(-x\)[/tex].
Putting these terms together, we get:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Now, match this with the options provided:
- A: [tex]\(9x^7 + 4x^{12} + 3x^3 - x\)[/tex]
- B: [tex]\(4x^{12} + 9x^7 + 3x^3 - x \)[/tex]
- C: [tex]\(3x^3 + 4x^{12} + 9x^7 - x\)[/tex]
- D: [tex]\(4x^{12} + 3x^3 - x + 9x^7\)[/tex]
The correct order in descending exponents matches with Option B: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
Here are the steps to write this polynomial in descending order:
1. Identify the exponents in each term:
- [tex]\( 4x^{12} \)[/tex] has an exponent of 12.
- [tex]\( 9x^7 \)[/tex] has an exponent of 7.
- [tex]\( 3x^3 \)[/tex] has an exponent of 3.
- [tex]\(-x\)[/tex] can be considered as [tex]\(-1x^1\)[/tex] with an exponent of 1.
2. Order the terms by their exponents from highest to lowest:
- The highest exponent is 12, then 7, followed by 3, and finally 1.
3. Arrange the terms based on the order identified:
- The term with the exponent of 12 is [tex]\( 4x^{12} \)[/tex].
- The term with the exponent of 7 is [tex]\( 9x^7 \)[/tex].
- The term with the exponent of 3 is [tex]\( 3x^3 \)[/tex].
- The term with the exponent of 1 is [tex]\(-x\)[/tex].
Putting these terms together, we get:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Now, match this with the options provided:
- A: [tex]\(9x^7 + 4x^{12} + 3x^3 - x\)[/tex]
- B: [tex]\(4x^{12} + 9x^7 + 3x^3 - x \)[/tex]
- C: [tex]\(3x^3 + 4x^{12} + 9x^7 - x\)[/tex]
- D: [tex]\(4x^{12} + 3x^3 - x + 9x^7\)[/tex]
The correct order in descending exponents matches with Option B: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
