Chapter 11.5, Problem 37PPS

To determine

To calculate: To find the quotient using long division method

Answer to Problem 37PPS

The quotient is $2c^2+c+2-\frac{1}{4c-2}$

Explanation of Solution

Given information: Expression $\left(8c^3+6c-5\right)÷\left(4c-2\right)$

Formula Used:

Long division is the division of whole number in a systematic procedure to derive the answer.

Calculation:

Expression is given as

  $\left(8c^3+6c-5\right)÷\left(4c-2\right)$

Dividing the polynomial with the divisor to derive the quotient and remainder

  $4c-2\begin{array}{c}\hfill 2c^2+c+2\\ \hfill \overline{)\begin{array}{l}8c^3+6c-5\\ 8c^3-4c^2\\ -\text{ +}\\ -------\\ 0+4c^2+6c\\ \text{ 4}{c}^2-2c\\ -+\\ -------\\ 0\text{ + }8c-5\\ \text{ +}8c-4\\ -\text{ +}\\ --------\\ -\text{1 }\end{array}}\end{array}$

Thus, quotient is $2c^2+c+2-\frac{1}{4c-2}$

Conclusion:

Hence, the quotient is $2c^2+c+2-\frac{1}{4c-2}$