Chapter 7.7, Problem 38E

To determine

To find: the value of $k$ .

Answer to Problem 38E

  $-20$

Explanation of Solution

Given information:

  $\left(x^2+8x+k\right)÷\left(x-2\right)$

Remainder is zero.

Calculation:

Simplify the expression by long division method as shown below.

  $x-2\begin{array}{c}\hfill x+10\\ \hfill \overline{)\begin{array}{l}{x}^2+8x+k\\ \underset{\_}{\begin{array}{l}{x}^2-2x\\ -+\end{array}}\\ 10x+k\\ 10x-20\\ \underset{\_}{-+}\\ k+20\end{array}}\end{array}$

Since the remainder is zero, so $k$ can be evaluated as follows:

  $\begin{array}{c}k+20=0\\ k=-20\left[\text{Subtract 20 from each side}\right]\end{array}$

Thus, the value of $k$ is $-20$ .