Answer :
To write a polynomial in descending order, we need to arrange its terms based on the exponents of the variable, starting with the highest and going down to the lowest.
Let's look at the given polynomial:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
Here are the steps to write this polynomial in descending order:
1. Identify the Exponents: Look at the exponents of each term:
- [tex]\(3x^3\)[/tex]: exponent is 3
- [tex]\(9x^7\)[/tex]: exponent is 7
- [tex]\(-x\)[/tex]: exponent is 1 (we can think of this as [tex]\(-1x^1\)[/tex])
- [tex]\(4x^{12}\)[/tex]: exponent is 12
2. Order the Terms by Exponent: Arrange the terms starting from the highest exponent to the lowest:
- The term with the highest exponent is [tex]\(4x^{12}\)[/tex].
- Next is [tex]\(9x^7\)[/tex].
- Then, we have [tex]\(3x^3\)[/tex].
- Finally, [tex]\(-x\)[/tex] (or [tex]\(-1x^1\)[/tex]) has the lowest exponent.
3. Write the Polynomial in Descending Order:
- Combine these terms in order:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Thus, the polynomial written in descending order by exponent is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Comparing this with the given options, the correct choice is:
D. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
Let's look at the given polynomial:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
Here are the steps to write this polynomial in descending order:
1. Identify the Exponents: Look at the exponents of each term:
- [tex]\(3x^3\)[/tex]: exponent is 3
- [tex]\(9x^7\)[/tex]: exponent is 7
- [tex]\(-x\)[/tex]: exponent is 1 (we can think of this as [tex]\(-1x^1\)[/tex])
- [tex]\(4x^{12}\)[/tex]: exponent is 12
2. Order the Terms by Exponent: Arrange the terms starting from the highest exponent to the lowest:
- The term with the highest exponent is [tex]\(4x^{12}\)[/tex].
- Next is [tex]\(9x^7\)[/tex].
- Then, we have [tex]\(3x^3\)[/tex].
- Finally, [tex]\(-x\)[/tex] (or [tex]\(-1x^1\)[/tex]) has the lowest exponent.
3. Write the Polynomial in Descending Order:
- Combine these terms in order:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Thus, the polynomial written in descending order by exponent is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Comparing this with the given options, the correct choice is:
D. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
