Questions: 15 p^7 + 9 p^4 / 3 p

Solution Steps

To divide the polynomial \(\frac{15 p^{7} + 9 p^{4}}{3 p}\), we need to divide each term in the numerator by the denominator separately.

1. Divide \(15 p^{7}\) by \(3 p\).
2. Divide \(9 p^{4}\) by \(3 p\).

We are given the expression to divide: \[ \frac{15 p^{7} + 9 p^{4}}{3 p} \]

We can split the numerator into two separate fractions: \[ \frac{15 p^{7}}{3 p} + \frac{9 p^{4}}{3 p} \]

Now, we simplify each fraction individually.

For the first fraction: \[ \frac{15 p^{7}}{3 p} = \frac{15}{3} \cdot \frac{p^{7}}{p} = 5 p^{6} \]

For the second fraction: \[ \frac{9 p^{4}}{3 p} = \frac{9}{3} \cdot \frac{p^{4}}{p} = 3 p^{3} \]

Combine the simplified terms to get the final result: \[ 5 p^{6} + 3 p^{3} \]

Final Answer