Answer :
To divide the polynomial [tex]\(12x^7 + 48x^6 - 54x^4 - 6x\)[/tex] by 6, follow these steps:
1. Break down the polynomial into individual terms:
- [tex]\(12x^7\)[/tex]
- [tex]\(48x^6\)[/tex]
- [tex]\(-54x^4\)[/tex]
- [tex]\(-6x\)[/tex]
2. Divide each term by 6:
- For the first term: [tex]\(\frac{12x^7}{6} = 2x^7\)[/tex]
- For the second term: [tex]\(\frac{48x^6}{6} = 8x^6\)[/tex]
- For the third term: [tex]\(\frac{-54x^4}{6} = -9x^4\)[/tex]
- For the fourth term: [tex]\(\frac{-6x}{6} = -x\)[/tex]
3. Combine the results into the new polynomial:
- The new polynomial is [tex]\(2x^7 + 8x^6 - 9x^4 - x\)[/tex].
Therefore, the resulting polynomial after dividing by 6 is:
[tex]\[2x^7 + 8x^6 - 9x^4 - x\][/tex]
This matches with the first option provided: [tex]\(2x^7 + 8x^6 - 9x^4 - x\)[/tex].
1. Break down the polynomial into individual terms:
- [tex]\(12x^7\)[/tex]
- [tex]\(48x^6\)[/tex]
- [tex]\(-54x^4\)[/tex]
- [tex]\(-6x\)[/tex]
2. Divide each term by 6:
- For the first term: [tex]\(\frac{12x^7}{6} = 2x^7\)[/tex]
- For the second term: [tex]\(\frac{48x^6}{6} = 8x^6\)[/tex]
- For the third term: [tex]\(\frac{-54x^4}{6} = -9x^4\)[/tex]
- For the fourth term: [tex]\(\frac{-6x}{6} = -x\)[/tex]
3. Combine the results into the new polynomial:
- The new polynomial is [tex]\(2x^7 + 8x^6 - 9x^4 - x\)[/tex].
Therefore, the resulting polynomial after dividing by 6 is:
[tex]\[2x^7 + 8x^6 - 9x^4 - x\][/tex]
This matches with the first option provided: [tex]\(2x^7 + 8x^6 - 9x^4 - x\)[/tex].
