Hello!
The answer is:
E. -2, 3, -3
Why?
To find the zeroes of the function, we just need to evaluate the given values and check if the function/expression tends to 0.
We are given the function
![f(x)=x^{3}+2x^{2}-9x-18](/tpl/images/0137/2940/29cf3.png)
Now, to find the zeroes, we need to substitute the values, so, substituting the values of the option E, we have:
First value, -2:
![f(-2)=-2^{3}+2*(-2)^{2}-9*(-2)-18](/tpl/images/0137/2940/090d5.png)
![f(-2)=-8+2*4+18-18](/tpl/images/0137/2940/1ebc4.png)
![f(-2)=-8+8+18-18=0](/tpl/images/0137/2940/29ca7.png)
Second value, 3:
![f(3)=3^{3}+2*(3)^{2}-9*(3)-18](/tpl/images/0137/2940/057fa.png)
![f(3)=27+2*9-27-18](/tpl/images/0137/2940/c1fb1.png)
![f(3)=27+18-27-18=0](/tpl/images/0137/2940/69c69.png)
Third value, -3:
![f(-3)=-3^{3}+2*-3^{2}-9*-3-18](/tpl/images/0137/2940/6ca09.png)
![f(-3)=-27+2*9+27-18](/tpl/images/0137/2940/335f0.png)
![f(-3)=-27+2*9+27-18=0](/tpl/images/0137/2940/a90a1.png)
Hence, we have that evaluating the values of the option E, the function tends to 0.
So, the correct option is: E. -2, 3, -3
Have a nice day!