The answer is the second one because if u plug in ⁿ and do the rest of the equation, you get your value
Answer:
A. 9
Step-by-step explanation:
We use the remainder theorem.
The given function is
![f(x) = {x}^{3} + 5 {x}^{2} + sx + 6](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%7Bx%7D%5E%7B3%7D%20%20%2B%205%20%7Bx%7D%5E%7B2%7D%20%20%2B%20sx%20%2B%206)
If this function is divisible by x+2, then by the remainder theorem,
![f( - 2) = 0](https://tex.z-dn.net/?f=f%28%20-%202%29%20%3D%200)
This implies that;
![{( - 2)}^{3} + 5( - 2 )^{2} + s( - 2) + 6 = 0](https://tex.z-dn.net/?f=%20%7B%28%20-%202%29%7D%5E%7B3%7D%20%20%2B%205%28%20-%202%20%29%5E%7B2%7D%20%20%2B%20s%28%20-%202%29%20%2B%206%20%3D%200)
We evaluate to get:
![- 8 + 20 - 2s + 6 = 0](https://tex.z-dn.net/?f=%20-%208%20%2B%2020%20-%202s%20%2B%206%20%3D%200)
![18 - 2s = 0](https://tex.z-dn.net/?f=%2018%20-%202s%20%3D%200)
![2s = 18 \\ s = 9](https://tex.z-dn.net/?f=2s%20%3D%2018%20%5C%5C%20s%20%3D%209)
It is a repeating decimal because 1/15=0.06...
90-3i I think sry if wrong