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Answer :
To divide the polynomial [tex]\(12x^7 + 48x^6 - 54x^4 - 6x\)[/tex] by 6, we need to divide each term individually by 6. Here’s how you do it step-by-step:
1. Divide the first term:
- The first term is [tex]\(12x^7\)[/tex].
- Divide [tex]\(12\)[/tex] by [tex]\(6\)[/tex], which gives [tex]\(2\)[/tex].
- So, the first term becomes [tex]\(2x^7\)[/tex].
2. Divide the second term:
- The second term is [tex]\(48x^6\)[/tex].
- Divide [tex]\(48\)[/tex] by [tex]\(6\)[/tex], which gives [tex]\(8\)[/tex].
- So, the second term becomes [tex]\(8x^6\)[/tex].
3. Divide the third term:
- The third term is [tex]\(-54x^4\)[/tex].
- Divide [tex]\(-54\)[/tex] by [tex]\(6\)[/tex], which gives [tex]\(-9\)[/tex].
- So, the third term becomes [tex]\(-9x^4\)[/tex].
4. Divide the fourth term:
- The fourth term is [tex]\(-6x\)[/tex].
- Divide [tex]\(-6\)[/tex] by [tex]\(6\)[/tex], which gives [tex]\(-1\)[/tex].
- So, the fourth term becomes [tex]\(-x\)[/tex].
After dividing each term by 6, the resulting polynomial is:
[tex]\[ 2x^7 + 8x^6 - 9x^4 - x \][/tex]
This matches one of the options you have, which is [tex]\(2x^7 + 8x^6 - 9x^4 - x\)[/tex]. So, this is the correct answer.
1. Divide the first term:
- The first term is [tex]\(12x^7\)[/tex].
- Divide [tex]\(12\)[/tex] by [tex]\(6\)[/tex], which gives [tex]\(2\)[/tex].
- So, the first term becomes [tex]\(2x^7\)[/tex].
2. Divide the second term:
- The second term is [tex]\(48x^6\)[/tex].
- Divide [tex]\(48\)[/tex] by [tex]\(6\)[/tex], which gives [tex]\(8\)[/tex].
- So, the second term becomes [tex]\(8x^6\)[/tex].
3. Divide the third term:
- The third term is [tex]\(-54x^4\)[/tex].
- Divide [tex]\(-54\)[/tex] by [tex]\(6\)[/tex], which gives [tex]\(-9\)[/tex].
- So, the third term becomes [tex]\(-9x^4\)[/tex].
4. Divide the fourth term:
- The fourth term is [tex]\(-6x\)[/tex].
- Divide [tex]\(-6\)[/tex] by [tex]\(6\)[/tex], which gives [tex]\(-1\)[/tex].
- So, the fourth term becomes [tex]\(-x\)[/tex].
After dividing each term by 6, the resulting polynomial is:
[tex]\[ 2x^7 + 8x^6 - 9x^4 - x \][/tex]
This matches one of the options you have, which is [tex]\(2x^7 + 8x^6 - 9x^4 - x\)[/tex]. So, this is the correct answer.
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