Chapter 4.3, Problem 16E

To determine

To divide: $\left(x^4+x^3-1\right)÷\left(x-2\right)$ using synthetic division.

Answer to Problem 16E

  $\begin{array}{l}Q\left(x\right)=x^3+3x^2+6x+12\\ R=23\end{array}$

Explanation of Solution

Given information: $\left(x^4+x^3-1\right)÷\left(x-2\right)$

Calculation:

  $\left(x^3-9x^2+27x-28\right)÷\left(x-3\right)$

After performing the synthetic procedure:

  $\begin{array}{l}-2|1\text{ 1 0 0 1}\\ |\underset{\_}{\text{ 2 6 12 24 }}\\ |\text{ 1 3 6 12 }|23\end{array}$

  $\begin{array}{l}Q\left(x\right)=x^3+3x^2+6x+12\\ R=23\end{array}$