Chapter 8.4, Problem 2WE

To determine

To divide : the given polynomial by the binomial using synthetic division.

Answer to Problem 2WE

  $\frac{2x^3-4x^2-7x+5}{x-3}=2x^2+2x-1+\frac{2}{x-3}$

Explanation of Solution

Given information :

The polynomial: $2x^3-4x^2-7x+5$

The binomial: $x-3$

Formula used : The divisor in a synthetic division is a binomial of the form $x-c$ .

Calculation :

As per the problem,

The dividend is $2x^3-4x^2-7x+5$

Since the divisor is $x-3$ , use $3$ for c . Note that the coefficient of $x^3$ is $2$

  $\begin{array}{l}\overline{)3}\text{ 2 }-4-75\\ \underset{\_}{\text{ 6 6 }-3}\\ \text{ 2 2 }-1\text{ | 2}\end{array}$

The quotient is $2x^2+2x-1$ , and the remainder is $2$

Therefore,

  $\frac{2x^3-4x^2-7x+5}{x-3}=2x^2+2x-1+\frac{2}{x-3}$