Answer :

To divide the expression [tex]\(\frac{27x^7 - 9x^4 + 15x^2}{3x}\)[/tex] and simplify it, follow these steps:

1. Separate the terms in the numerator:
The expression in the numerator is a polynomial: [tex]\(27x^7 - 9x^4 + 15x^2\)[/tex].

2. Divide each term individually by the denominator [tex]\(3x\)[/tex]:
- Divide the first term: [tex]\(\frac{27x^7}{3x} = 9x^{7-1} = 9x^6\)[/tex].
- Divide the second term: [tex]\(\frac{-9x^4}{3x} = -3x^{4-1} = -3x^3\)[/tex].
- Divide the third term: [tex]\(\frac{15x^2}{3x} = 5x^{2-1} = 5x\)[/tex].

3. Combine all the results:
Arrange the quotient from each term together, so you get:
[tex]\(9x^6 - 3x^3 + 5x\)[/tex].

4. Simplified expression:
The simplified expression is:
[tex]\[
x(9x^5 - 3x^2 + 5)
\][/tex]

This is the result when [tex]\(\frac{27x^7 - 9x^4 + 15x^2}{3x}\)[/tex] is divided and simplified.

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