Find the quotient of minus, 9, x, cubed, plus, 9, x, squared, plus, 9−9x
3
+9x
2
+9 divided by 33.

To find the quotient of the expression \(-9x^3 + 9x^2 + 9 - 9x\) divided by 33, we divide each term of the polynomial by 33.

\[
\text{Quotient} = \frac{-9x^3}{33} + \frac{9x^2}{33} + \frac{-9x}{33} + \frac{9}{33}
\]

Simplifying each term:

1. \(\frac{-9x^3}{33} = \frac{-9}{33}x^3 = -\frac{1}{11}x^3\)
2. \(\frac{9x^2}{33} = \frac{9}{33}x^2 = \frac{1}{11}x^2\)
3. \(\frac{-9x}{33} = \frac{-9}{33}x = -\frac{1}{11}x\)
4. \(\frac{9}{33} = \frac{1}{11}\)

So, the quotient is:

\[
-\frac{1}{11}x^3 + \frac{1}{11}x^2 - \frac{1}{11}x + \frac{1}{11}
\]

Would you like further details or explanations?

Here are five related questions:
1. How would the quotient change if the divisor was 11 instead of 33?
2. What is the remainder if we divide \(-9x^3 + 9x^2 + 9 - 9x\) by 33?
3. How do you interpret the coefficients after dividing by 33?
4. How do you check the correctness of this quotient?
5. What is the result of dividing \(-9x^3 + 9x^2 + 9 - 9x\) by \(-33\) instead of 33?

**Tip:** Always simplify fractions as much as possible when dividing polynomials by constants to get the simplest form of the quotient.

Learn how to find the quotient of the polynomial -9x^3 + 9x^2 + 9 - 9x divided by 33. This problem involves dividing a polynomial by a constant, simplifying each term step-by-step. Suitable for high school students studying polynomials and algebra.

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