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Answer :
Let's solve the problem step-by-step:
We need to subtract the second polynomial from the first:
1. Write down the given polynomials:
First Polynomial: [tex]\(-3x^7 + 6x^9 - 7 + 6x^8\)[/tex]
Second Polynomial: [tex]\(-5 - 9x^8 + 2x^9 + 9x^7\)[/tex]
2. Set up the subtraction:
[tex]\[
\left(-3x^7 + 6x^9 - 7 + 6x^8\right) - \left(-5 - 9x^8 + 2x^9 + 9x^7\right)
\][/tex]
3. Distribute the negative sign to the second polynomial:
[tex]\[
-3x^7 + 6x^9 - 7 + 6x^8 + 5 + 9x^8 - 2x^9 - 9x^7
\][/tex]
4. Combine like terms:
- For [tex]\(x^9\)[/tex]: [tex]\(6x^9 - 2x^9 = 4x^9\)[/tex]
- For [tex]\(x^8\)[/tex]: [tex]\(6x^8 + 9x^8 = 15x^8\)[/tex]
- For [tex]\(x^7\)[/tex]: [tex]\(-3x^7 - 9x^7 = -12x^7\)[/tex]
- For the constant terms: [tex]\(-7 + 5 = -2\)[/tex]
5. Write the simplified expression:
[tex]\[
4x^9 + 15x^8 - 12x^7 - 2
\][/tex]
6. Find the answer that matches this expression:
The correct answer is:
C. [tex]\(4x^9 + 15x^8 - 12x^7 - 2\)[/tex]
We need to subtract the second polynomial from the first:
1. Write down the given polynomials:
First Polynomial: [tex]\(-3x^7 + 6x^9 - 7 + 6x^8\)[/tex]
Second Polynomial: [tex]\(-5 - 9x^8 + 2x^9 + 9x^7\)[/tex]
2. Set up the subtraction:
[tex]\[
\left(-3x^7 + 6x^9 - 7 + 6x^8\right) - \left(-5 - 9x^8 + 2x^9 + 9x^7\right)
\][/tex]
3. Distribute the negative sign to the second polynomial:
[tex]\[
-3x^7 + 6x^9 - 7 + 6x^8 + 5 + 9x^8 - 2x^9 - 9x^7
\][/tex]
4. Combine like terms:
- For [tex]\(x^9\)[/tex]: [tex]\(6x^9 - 2x^9 = 4x^9\)[/tex]
- For [tex]\(x^8\)[/tex]: [tex]\(6x^8 + 9x^8 = 15x^8\)[/tex]
- For [tex]\(x^7\)[/tex]: [tex]\(-3x^7 - 9x^7 = -12x^7\)[/tex]
- For the constant terms: [tex]\(-7 + 5 = -2\)[/tex]
5. Write the simplified expression:
[tex]\[
4x^9 + 15x^8 - 12x^7 - 2
\][/tex]
6. Find the answer that matches this expression:
The correct answer is:
C. [tex]\(4x^9 + 15x^8 - 12x^7 - 2\)[/tex]
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