Factorize `9z^3-27 z^2-100 z+300 ,` if it is given that `(3z+10)` is a factor of it.

Explanation

To factorize the polynomial \( 9z^3 - 27z^2 - 100z + 300 \) given that \( (3z + 10) \) is a factor, we can follow these steps:

### Step 1: Polynomial Long Division
Since \( (3z + 10) \) is a factor, we can perform polynomial long division of \( 9z^3 - 27z^2 - 100z + 300 \) by \( 3z + 10 \).

1. **Divide the leading term**: Divide the leading term of the polynomial \( 9z^3 \) by the leading term of the divisor \( 3z \):
\[
\frac{9z^3}{3z} = 3z^2
...