College

Divide: [tex](72 x^9 - 36 x^6 + 27 x^3) \div 9 x^3[/tex]

A. [tex]8 x^9 - 4 x^6 + 3 x^3[/tex]

B. [tex]72 x^6 - 36 x^3 + 27[/tex]

C. [tex]8 x^6 - 36 x^6 + 27 x^3[/tex]

D. [tex]8 x^6 - 4 x^3 + 3[/tex]

Answer :

To divide
[tex]$$72x^9 - 36x^6 + 27x^3$$[/tex]
by
[tex]$$9x^3,$$[/tex]
we can divide each term in the numerator by the divisor.

1. For the first term:
[tex]$$\frac{72x^9}{9x^3} = \frac{72}{9}x^{9-3} = 8x^6.$$[/tex]

2. For the second term:
[tex]$$\frac{-36x^6}{9x^3} = -\frac{36}{9}x^{6-3} = -4x^3.$$[/tex]

3. For the third term:
[tex]$$\frac{27x^3}{9x^3} = \frac{27}{9}x^{3-3} = 3x^0 = 3.$$[/tex]

Putting the results together, the quotient is:
[tex]$$8x^6 - 4x^3 + 3.$$[/tex]

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