Chapter 8.4, Problem 12WE

To determine

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

Answer to Problem 12WE

  $\frac{3x^6-2x^5-x^4-x^2-2x+3}{x-1}=3x^5+x^4-x-3$

Explanation of Solution

Given information :

The polynomial: $3x^6-2x^5-x^4-x^2-2x+3$

The binomial: $x-1$

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

Calculation :

As per the problem,

The dividend is $3x^6-2x^5-x^4-x^2-2x+3$ . Insert the missing term $0x^3$ .

Since the divisor is $x-1$ , use $1$ for c .

  $\begin{array}{l}\overline{)1}\text{ 3 }-\text{2 }-\text{1 0 }-1-2\text{ 3}\\ \underset{\_}{\text{ 3 1 0 0 }-1-3}\\ \text{ 3 }1\text{ 0 0 }-1-3\text{ | 0}\end{array}$

The quotient is $3x^5+x^4-x-3$ , and the remainder is $0$

Therefore,

  $\frac{3x^6-2x^5-x^4-x^2-2x+3}{x-1}=3x^5+x^4-x-3$