Divide : `9a^(5) - 6a^(2)` by `3a^(2)`

Answer

To divide the expression \(9a^5 - 6a^2\) by \(3a^2\), we can follow these steps:

### Step 1: Write the division in fraction form
We start by writing the expression as a fraction:
\[ \frac{9a^5 - 6a^2}{3a^2} \]

### Step 2: Split the fraction
We can split the fraction into two separate fractions:
\[ \frac{9a^5}{3a^2} - \frac{6a^2}{3a^2} \]

### Step 3: Simplify each fraction
Now, we simplify each fraction separately.

For the first fraction:
\[ \frac{9a^5}{3a^2} = \frac{9}{3} \cdot \frac{a^5}{a^2} = 3a^{5-2} = 3a^3 \]

For the second fraction:
\[ \frac{6a^2}{3a^2} = \frac{6}{3} \cdot \frac{a^2}{a^2} = 2 \cdot 1 = 2 \]

### Step 4: Combine the results
Now we combine the results from the two fractions:
\[ 3a^3 - 2 \]

### Final Answer
Thus, the final result of dividing \(9a^5 - 6a^2\) by \(3a^2\) is:
\[ 3a^3 - 2 \]

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