Chapter 8.4, Problem 1WE

To determine

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

Answer to Problem 1WE

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

Explanation of Solution

Given information :

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

The binomial: $x-2$

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

Calculation :

As per the problem,

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

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

  $\begin{array}{l}\overline{)2}\text{ 3 }-51-2\\ \underset{\_}{\text{ 6 2 6}}\\ \text{ 3 1 3 | }4\end{array}$

The quotient is $3x^2+x+3$ , and the remainder is $4$

Therefore,

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