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Answer :
To find the polynomial that represents the difference [tex]\((x^7 + 4x^6 - x^2 + 2) - (2x^6 + 3x^5 + x^2 - 6x)\)[/tex], follow these steps:
1. Write the first polynomial:
- [tex]\(x^7 + 4x^6 - x^2 + 2\)[/tex]
2. Write the second polynomial:
- [tex]\(2x^6 + 3x^5 + x^2 - 6x\)[/tex]
3. Subtract the second polynomial from the first:
- Subtract the coefficients of like terms:
- For [tex]\(x^7\)[/tex]: [tex]\(1 - 0 = 1\)[/tex]
- For [tex]\(x^6\)[/tex]: [tex]\(4 - 2 = 2\)[/tex]
- For [tex]\(x^5\)[/tex]: [tex]\(0 - 3 = -3\)[/tex]
- For [tex]\(x^2\)[/tex]: [tex]\(-1 - 1 = -2\)[/tex]
- For [tex]\(x^1\)[/tex]: [tex]\(0 - (-6) = 6\)[/tex]
- Constant term: [tex]\(2 - 0 = 2\)[/tex]
4. Combine the results:
[tex]\(x^7 + 2x^6 - 3x^5 - 2x^2 + 6x + 2\)[/tex]
Thus, the polynomial representing the difference is:
A. [tex]\(x^7 + 2x^6 - 3x^5 - 2x^2 + 6x + 2\)[/tex]
1. Write the first polynomial:
- [tex]\(x^7 + 4x^6 - x^2 + 2\)[/tex]
2. Write the second polynomial:
- [tex]\(2x^6 + 3x^5 + x^2 - 6x\)[/tex]
3. Subtract the second polynomial from the first:
- Subtract the coefficients of like terms:
- For [tex]\(x^7\)[/tex]: [tex]\(1 - 0 = 1\)[/tex]
- For [tex]\(x^6\)[/tex]: [tex]\(4 - 2 = 2\)[/tex]
- For [tex]\(x^5\)[/tex]: [tex]\(0 - 3 = -3\)[/tex]
- For [tex]\(x^2\)[/tex]: [tex]\(-1 - 1 = -2\)[/tex]
- For [tex]\(x^1\)[/tex]: [tex]\(0 - (-6) = 6\)[/tex]
- Constant term: [tex]\(2 - 0 = 2\)[/tex]
4. Combine the results:
[tex]\(x^7 + 2x^6 - 3x^5 - 2x^2 + 6x + 2\)[/tex]
Thus, the polynomial representing the difference is:
A. [tex]\(x^7 + 2x^6 - 3x^5 - 2x^2 + 6x + 2\)[/tex]
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