Chapter 11.5, Problem 5BCYP

To determine

To calculate: To find the quotient $\left(x^4+2x^3+6x-10\right)÷\left(x+2\right)$

Answer to Problem 5BCYP

The quotient is $x^3+6-\frac{22}{x+2}$

Explanation of Solution

Given information: Expression $\left(x^4+2x^3+6x-10\right)÷\left(x+2\right)$

Formula Used:

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

Calculation:

Expression is given as

  $\left(x^4+2x^3+6x-10\right)÷\left(x+2\right)$

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

  $x+2\begin{array}{c}\hfill x^3+6\\ \hfill \overline{)\begin{array}{l}{x}^4+2x^3+6x-10\\ x^4+2x^3\\ --\\ ----------\\ 0+0\\ +6x-10\\ \text{ +6}x+12\\ --\\ ----------\\ -\text{22}\end{array}}\end{array}$

Thus, quotient is $x^3+6-\frac{22}{x+2}$

Conclusion:

Hence, the quotient is $x^3+6-\frac{22}{x+2}$