To determine the quotient of the expression
[tex]\[
\left(15n^2 - 27n\right) \div 3n
\][/tex]
we can follow these steps:
1. Divide each term in the numerator by the term in the denominator individually:
- The first term in the numerator is [tex]\(15n^2\)[/tex]:
[tex]\[
\frac{15n^2}{3n}
\][/tex]
Simplifying this term:
[tex]\[
\frac{15n^2}{3n} = 5n \quad \text{(since } 15 ÷ 3 = 5 \text{ and } n^2 ÷ n = n \text{)}
\][/tex]
- The second term in the numerator is [tex]\(-27n\)[/tex]:
[tex]\[
\frac{-27n}{3n}
\][/tex]
Simplifying this term:
[tex]\[
\frac{-27n}{3n} = -9 \quad \text{(since } -27 ÷ 3 = -9 \text{ and } n ÷ n = 1 \text{)}
\][/tex]
2. Combine these simplified terms:
- The resulting expression becomes:
[tex]\[
5n - 9
\][/tex]
Therefore, the quotient of the given expression is:
[tex]\[
\boxed{5n - 9}
\][/tex]
