# How do you determine the value of k if the remainder is 3 given (x^3+kx^2+x+5) div(x+2)?

Feb 13, 2017

The answer is $k = 2$

#### Explanation:

Let $f \left(x\right) = {x}^{3} + k {x}^{2} + x + 5$

When $f \left(x\right)$ is divided by $\left(x + 2\right)$ , the remainder is $= 3$

This is the remainder theorem

so,

$f \left(- 2\right) = - 8 + 4 k - 2 + 5 = 3$

$4 k = 3 + 5 = 8$

$k = 2$