Chapter 14.3, Problem 1MRE

To determine

To find: The quotient and the remainder.

Answer to Problem 1MRE

Quotient is $x^3-2x^2+2x-4$ and remainder is $11$ .

Explanation of Solution

Given information:

An expression is given as −

  $\frac{x^4-2x^2+3}{x+2}$

Calculation:

Given expression is $\frac{x^4-2x^2+3}{x+2}$ .

Applying common division method −

  $x+2\begin{array}{c}\hfill x^3-2x^2+2x-4\\ \hfill \overline{)\begin{array}{l}{x}^4-2x^2+3\\ \frac{\begin{array}{l}{x}^4+2x^3\\ --\end{array}}{\begin{array}{l}-2x^3-2x^2\\ \frac{\begin{array}{l}-2x^3-4x^2\\ ++\end{array}}{\begin{array}{l}2x^2+3\\ 2x^2+4x\\ \frac{--}{\begin{array}{l}-4x+3\\ -4x-8\\ \frac{++}{11}\end{array}}\end{array}}\end{array}}\end{array}}\end{array}$

Hence, quotient is $x^3-2x^2+2x-4$ and remainder is $11$ .