Chapter 8.6, Problem 2ST

To determine

To divide the expression using synthetic division.

Answer to Problem 2ST

Therefore the quotient of the division is $3x^3+x^2+2x-1+\frac{2}{x-2}$

Explanation of Solution

Given information:

The given expression is $2x^4-3x^3-5x+4$ , and the divisor is $x-2$ .

Calculation :

Start synthetic division.

  $\begin{array}{l}\text{2 }\overline{)\begin{array}{l}\text{2 }-\text{3 0 }-\text{5 4}\\ \text{ 4 2 4 }-2\end{array}}\\ \text{ 2 1 2 }-\text{1 2}\end{array}$

Therefore the quotient of the division is $3x^3+x^2+2x-1+\frac{2}{x-2}$