#### Answer

Fill the blanks in with :
9 ... $(3x-5)$ ... $9$ ...
... $3x-5+\displaystyle \frac{9}{2x+1}$

#### Work Step by Step

Long Division of Polynomials
1. Arrange ...
2. Divide ...
3. Multiply ...
4. Subtract the product from the dividend.
5. Bring down the next term in the original dividend and write it next to the
remainder to form a new dividend.
6. Use this new expression as the dividend and repeat this process until the
remainder can no longer be divided. This will occur when the degree of the
remainder (the highest exponent on a variable in the remainder) is less than
the degree of the divisor.
----------
So, subtracting the product $(-10-5)$
from the dividend $(-10x+4)$
we obtain $+9=9$
Thus, the quotient is $(3x-5) $remainder is $9.$
The answer to $(6x^{2} -7x+4)\div(2x+1)$ is written as
$3x-5+\displaystyle \frac{9}{2x+1}$