If (x+2) is a factor of x^3-6x^2+kx+10, what is k?

Jan 30, 2017

The answer is $k = - 11$

Explanation:

Let $f \left(x\right) = {x}^{3} - 6 {x}^{2} + k x + 10$

If $\left(x + 2\right)$ is a factor

Then,

$f \left(- 2\right) = 0$

$f \left(- 2\right) = - 8 - 24 - 2 k + 10 = 0$

$2 k = - 22$

$k = - 11$