Chapter 4.3, Problem 39E

To determine

To find: The value of k so that $\left(x^3+18x^2+kx+4\right)÷\left(x+2\right)$ remainder is zero.

Answer to Problem 39E

  $k=34$

Explanation of Solution

Given information: $\left(x^3+18x^2+kx+4\right)÷\left(x+2\right)$

Calculation:

  $\left(x^3+18x^2+kx+4\right)÷\left(x+2\right)$

If the remainder is equal to 0 then $x+2$ must be a factor and $f\left(-2\right)=0$

  $f\left(-2\right)={\left(-2\right)}^3+18{\left(-2\right)}^2+k\left(-2\right)+4=0$

Solve for k.

  $\Rightarrow k=34$