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Answer :
To solve the question of ordering the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] in descending order by the exponent, follow these steps:
1. Identify the terms of the polynomial:
- [tex]\(3x^3\)[/tex]
- [tex]\(9x^7\)[/tex]
- [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex])
- [tex]\(4x^{12}\)[/tex]
2. Order the terms by their exponents:
- Look at the exponent of each term to identify their order. The term with the highest exponent should come first.
- The exponents in the terms are: 12 (for [tex]\(4x^{12}\)[/tex]), 7 (for [tex]\(9x^7\)[/tex]), 3 (for [tex]\(3x^3\)[/tex]), and 1 (for [tex]\(-x\)[/tex]).
3. Write the polynomial in descending order of the exponents:
- Start with the term that has the highest exponent:
- [tex]\(4x^{12}\)[/tex]
- Next is [tex]\(9x^7\)[/tex] since 7 is the next largest exponent.
- Then [tex]\(3x^3\)[/tex] with exponent 3.
- Finally, [tex]\(-x\)[/tex], with the exponent of 1.
4. Combine these ordered terms:
- [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
Thus, the polynomial in descending order is: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
The correct choice from the given options is B.
1. Identify the terms of the polynomial:
- [tex]\(3x^3\)[/tex]
- [tex]\(9x^7\)[/tex]
- [tex]\(-x\)[/tex] (which is [tex]\(-1x^1\)[/tex])
- [tex]\(4x^{12}\)[/tex]
2. Order the terms by their exponents:
- Look at the exponent of each term to identify their order. The term with the highest exponent should come first.
- The exponents in the terms are: 12 (for [tex]\(4x^{12}\)[/tex]), 7 (for [tex]\(9x^7\)[/tex]), 3 (for [tex]\(3x^3\)[/tex]), and 1 (for [tex]\(-x\)[/tex]).
3. Write the polynomial in descending order of the exponents:
- Start with the term that has the highest exponent:
- [tex]\(4x^{12}\)[/tex]
- Next is [tex]\(9x^7\)[/tex] since 7 is the next largest exponent.
- Then [tex]\(3x^3\)[/tex] with exponent 3.
- Finally, [tex]\(-x\)[/tex], with the exponent of 1.
4. Combine these ordered terms:
- [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
Thus, the polynomial in descending order is: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
The correct choice from the given options is B.
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