Explanation

To find the quotient, perform polynomial long division:

Divide 6n² + 5n + 12 by 2n + 3:

6n² + 5n + 12 | 2n + 3

First, divide 6n² by 2n:

3n

Multiply 2n + 3 by 3n:

6n² + 9n

Subtract this from the original polynomial:

-4n + 12

Now, divide -4n by 2n:

-2

Multiply 2n + 3 by -2:

-4n - 6

Subtract this from -4n + 12:

18

Since 18 is a constant and cannot be divided by 2n + 3, the remainder is 18.

The quotient is:

3n - 2