Chapter 8.6, Problem 1ST

To determine

To divide: The divide the given expression.

Answer to Problem 1ST

The quotient is $x^2-2x+3$

Explanation of Solution

Given information:

The expression is given as;

  $\frac{x^4+x^3-5x^2+13x-6}{x^2+3x-2}$

Calculation:

The expression can be divided as:

  $\begin{array}{l}{x}^2+3x-2\begin{array}{c}\hfill x^2-2x+3\\ \hfill \overline{)x^4+x^3-5x^2+13x-6}\end{array}\\ \underset{\_}{x^4+3x^3-2x^2}\\ -2x^3-3x^2+13x\\ \underset{\_}{-2x^3-6x^2+4x}\\ \text{ 3}{x}^2+9x-6\\ \underset{\_}{\text{ 3}{x}^2+9x-6}\\ \text{ 0}\end{array}$

Therefore,

The quotient is $x^2-2x+3$