Answer :
To divide the polynomial [tex]\((-12x^9 + 3x^7 + 24x^6)\)[/tex] by [tex]\(6x\)[/tex], we need to divide each term of the polynomial by [tex]\(6x\)[/tex].
1. Divide [tex]\(-12x^9\)[/tex] by [tex]\(6x\)[/tex]:
[tex]\[ \frac{-12x^9}{6x} = -2x^{9-1} = -2x^8 \][/tex]
2. Divide [tex]\(3x^7\)[/tex] by [tex]\(6x\)[/tex]:
[tex]\[ \frac{3x^7}{6x} = \frac{3}{6}x^{7-1} = \frac{1}{2}x^6 \][/tex]
3. Divide [tex]\(24x^6\)[/tex] by [tex]\(6x\)[/tex]:
[tex]\[ \frac{24x^6}{6x} = 4x^{6-1} = 4x^5 \][/tex]
Putting it all together, the quotient is:
[tex]\[ -2x^8 + \frac{1}{2}x^6 + 4x^5 \][/tex]
The correct option that matches this result is:
C. [tex]\(-2x^8 + \frac{1}{2}x^6 + 4x^5\)[/tex]
1. Divide [tex]\(-12x^9\)[/tex] by [tex]\(6x\)[/tex]:
[tex]\[ \frac{-12x^9}{6x} = -2x^{9-1} = -2x^8 \][/tex]
2. Divide [tex]\(3x^7\)[/tex] by [tex]\(6x\)[/tex]:
[tex]\[ \frac{3x^7}{6x} = \frac{3}{6}x^{7-1} = \frac{1}{2}x^6 \][/tex]
3. Divide [tex]\(24x^6\)[/tex] by [tex]\(6x\)[/tex]:
[tex]\[ \frac{24x^6}{6x} = 4x^{6-1} = 4x^5 \][/tex]
Putting it all together, the quotient is:
[tex]\[ -2x^8 + \frac{1}{2}x^6 + 4x^5 \][/tex]
The correct option that matches this result is:
C. [tex]\(-2x^8 + \frac{1}{2}x^6 + 4x^5\)[/tex]
