Answer:
[tex]k\text{ = 10}[/tex]
Explanation:
For (x+2) to be a factor of the polynomial, if we set x+2 to 0, then substitute the value for x, we would get 0
Mathematically, we have it that:
[tex]\begin{gathered} x+2\text{ = 0} \\ x\text{ = -2} \end{gathered}[/tex]
We can now proceed to substitute -2 into the polynomial as follows:
[tex]\begin{gathered} (-2)^3-6(-2_{})^2-11(-2)+k\text{ = 0} \\ -8-24+22+k\text{ = 0} \\ -32+22+k\text{ = 0} \\ k\text{ = 32-22} \\ k\text{ = 10} \end{gathered}[/tex]
