Answer :
To write a polynomial in descending order, we arrange the terms from the highest exponent to the lowest exponent. This helps to clearly identify the leading term and follow a standard format.
Let's rewrite the given polynomial:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
Step-by-step solution:
1. Identify the exponents:
- The exponents in the polynomial are 3, 7, 1 (for [tex]\(-x\)[/tex], which is [tex]\(x^1\)[/tex]), and 12.
2. Arrange from highest to lowest exponent:
- The term with the highest exponent is [tex]\(4x^{12}\)[/tex].
- Next is [tex]\(9x^7\)[/tex], with the exponent 7.
- Then [tex]\(3x^3\)[/tex], with the exponent 3.
- Finally, [tex]\(-x\)[/tex], which has an exponent of 1.
3. Write the polynomial in descending order:
- Put the terms in order: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
Looking at the options provided:
A. [tex]\(3x^3 + 4x^{12} + 9x^7 - x\)[/tex]
B. [tex]\(4x^{12} + 3x^3 - x + 9x^7\)[/tex]
C. [tex]\(9x^7 + 4x^{12} + 3x^3 - x\)[/tex]
D. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
The correct answer is D: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
This order correctly follows the descending powers of [tex]\(x\)[/tex].
Let's rewrite the given polynomial:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
Step-by-step solution:
1. Identify the exponents:
- The exponents in the polynomial are 3, 7, 1 (for [tex]\(-x\)[/tex], which is [tex]\(x^1\)[/tex]), and 12.
2. Arrange from highest to lowest exponent:
- The term with the highest exponent is [tex]\(4x^{12}\)[/tex].
- Next is [tex]\(9x^7\)[/tex], with the exponent 7.
- Then [tex]\(3x^3\)[/tex], with the exponent 3.
- Finally, [tex]\(-x\)[/tex], which has an exponent of 1.
3. Write the polynomial in descending order:
- Put the terms in order: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
Looking at the options provided:
A. [tex]\(3x^3 + 4x^{12} + 9x^7 - x\)[/tex]
B. [tex]\(4x^{12} + 3x^3 - x + 9x^7\)[/tex]
C. [tex]\(9x^7 + 4x^{12} + 3x^3 - x\)[/tex]
D. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
The correct answer is D: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
This order correctly follows the descending powers of [tex]\(x\)[/tex].
