Questions: Divide the polynomial by the monomial. (Simplify your answer completely.) (3c^5 + 9c^4 - 12c^3 - 21c) / (3c^2)

Solution Steps

To divide the polynomial by the monomial, we need to divide each term of the polynomial by the monomial separately. Simplify each resulting term to get the final answer.

We start with the expression

\[ \frac{3c^{5} + 9c^{4} - 12c^{3} - 21c}{3c^{2}}. \]

To simplify, we divide each term in the numerator by the monomial \(3c^{2}\).

Dividing each term gives us:

\[ \frac{3c^{5}}{3c^{2}} + \frac{9c^{4}}{3c^{2}} - \frac{12c^{3}}{3c^{2}} - \frac{21c}{3c^{2}}. \]

This simplifies to:

\[ c^{3} + 3c^{2} - 4c - \frac{7}{c}. \]

Final Answer