Answer :
To divide the polynomial [tex]\(12x^7 + 48x^6 - 54x^4 - 6x\)[/tex] by 2, you simply divide each coefficient in the polynomial by 2. Let's go through it step by step:
1. The original polynomial is [tex]\(12x^7 + 48x^6 - 54x^4 - 6x\)[/tex].
2. Identify the coefficients of each term:
- The coefficient of [tex]\(x^7\)[/tex] is 12.
- The coefficient of [tex]\(x^6\)[/tex] is 48.
- The coefficient of [tex]\(x^4\)[/tex] is -54.
- The coefficient of [tex]\(x\)[/tex] is -6.
- The polynomial does not include terms for [tex]\(x^5\)[/tex], [tex]\(x^3\)[/tex], or a constant term, so their coefficients are 0.
3. Divide each coefficient by 2:
- For [tex]\(x^7\)[/tex]: [tex]\( \frac{12}{2} = 6\)[/tex]
- For [tex]\(x^6\)[/tex]: [tex]\( \frac{48}{2} = 24\)[/tex]
- For [tex]\(x^5\)[/tex]: [tex]\( \frac{0}{2} = 0\)[/tex]
- For [tex]\(x^4\)[/tex]: [tex]\( \frac{-54}{2} = -27\)[/tex]
- For [tex]\(x^3\)[/tex]: [tex]\( \frac{0}{2} = 0\)[/tex]
- For [tex]\(x^2\)[/tex]: [tex]\( \frac{0}{2} = 0\)[/tex]
- For [tex]\(x\)[/tex]: [tex]\( \frac{-6}{2} = -3\)[/tex]
- For the constant term (no x): [tex]\( \frac{0}{2} = 0\)[/tex]
4. Write the resulting polynomial with the new coefficients:
- The result is [tex]\(6x^7 + 24x^6 - 27x^4 - 3x\)[/tex].
So, the polynomial [tex]\(12x^7 + 48x^6 - 54x^4 - 6x\)[/tex] divided by 2 is [tex]\(6x^7 + 24x^6 - 27x^4 - 3x\)[/tex].
1. The original polynomial is [tex]\(12x^7 + 48x^6 - 54x^4 - 6x\)[/tex].
2. Identify the coefficients of each term:
- The coefficient of [tex]\(x^7\)[/tex] is 12.
- The coefficient of [tex]\(x^6\)[/tex] is 48.
- The coefficient of [tex]\(x^4\)[/tex] is -54.
- The coefficient of [tex]\(x\)[/tex] is -6.
- The polynomial does not include terms for [tex]\(x^5\)[/tex], [tex]\(x^3\)[/tex], or a constant term, so their coefficients are 0.
3. Divide each coefficient by 2:
- For [tex]\(x^7\)[/tex]: [tex]\( \frac{12}{2} = 6\)[/tex]
- For [tex]\(x^6\)[/tex]: [tex]\( \frac{48}{2} = 24\)[/tex]
- For [tex]\(x^5\)[/tex]: [tex]\( \frac{0}{2} = 0\)[/tex]
- For [tex]\(x^4\)[/tex]: [tex]\( \frac{-54}{2} = -27\)[/tex]
- For [tex]\(x^3\)[/tex]: [tex]\( \frac{0}{2} = 0\)[/tex]
- For [tex]\(x^2\)[/tex]: [tex]\( \frac{0}{2} = 0\)[/tex]
- For [tex]\(x\)[/tex]: [tex]\( \frac{-6}{2} = -3\)[/tex]
- For the constant term (no x): [tex]\( \frac{0}{2} = 0\)[/tex]
4. Write the resulting polynomial with the new coefficients:
- The result is [tex]\(6x^7 + 24x^6 - 27x^4 - 3x\)[/tex].
So, the polynomial [tex]\(12x^7 + 48x^6 - 54x^4 - 6x\)[/tex] divided by 2 is [tex]\(6x^7 + 24x^6 - 27x^4 - 3x\)[/tex].
