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What is the quotient when [tex](-12x^9 + 3x^7 + 24x^6)[/tex] is divided by [tex]6x[/tex]?

A. [tex]2x^8 + \frac{1}{2}x^6 + 4x^5[/tex]
B. [tex]-2x^8 + \frac{1}{2}x^6 + 4x^5[/tex]
C. [tex]2x^9 + 2x^7 + 4x^6[/tex]
D. [tex]-2x^8 + 2x^6 + 4x^5[/tex]

Answer :

We want to divide
[tex]$$-12x^9 + 3x^7 + 24x^6$$[/tex]
by
[tex]$$6x.$$[/tex]

To do this, we divide each term in the polynomial by [tex]$6x$[/tex].

1. For the term [tex]$-12x^9$[/tex]:
[tex]$$\frac{-12x^9}{6x} = \frac{-12}{6}x^{9-1} = -2x^8.$$[/tex]

2. For the term [tex]$3x^7$[/tex]:
[tex]$$\frac{3x^7}{6x} = \frac{3}{6}x^{7-1} = \frac{1}{2}x^6.$$[/tex]

3. For the term [tex]$24x^6$[/tex]:
[tex]$$\frac{24x^6}{6x} = \frac{24}{6}x^{6-1} = 4x^5.$$[/tex]

Thus, the quotient is
[tex]$$-2x^8 + \frac{1}{2}x^6 + 4x^5.$$[/tex]

Comparing with the given choices, the correct answer is option B.

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