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Determine the quotient of the following expression.

[tex]\[ \left(15n^2 - 27n\right) \div 3n \][/tex]

Write the quotient in standard form with the term of largest degree on the left.



Answer :

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]