Answer:
![3(x - 2) (x^2 + 3x + 6)\\](https://tex.z-dn.net/?f=3%28x%20-%202%29%20%28x%5E2%20%2B%203x%20%2B%206%29%5C%5C)
Step-by-step explanation:
Firstly, divide all parts of the equation by 3:
![3x^3 + 3x^2-36](https://tex.z-dn.net/?f=3x%5E3%20%2B%203x%5E2-36)
![3(x^3 + x^2-12)](https://tex.z-dn.net/?f=3%28x%5E3%20%2B%20x%5E2-12%29)
Now focus on the equation:
![x^3 + x^2-12](https://tex.z-dn.net/?f=x%5E3%20%2B%20x%5E2-12)
We know that the equation can be factored using x so we know that (x +- unknown) is the factor. We need to find the easiest way to factor this, lets find the factors of 12:
1 12
2 6
3 4
1 and 12 won't work so let's try 2 and 6, initially start as a negative 2:
= ![x^2 + 3x + 6](https://tex.z-dn.net/?f=x%5E2%20%2B%203x%20%2B%206)
We can confirm this is simplified by multiplying together:
![(x - 2) (x^2 + 3x + 6)](https://tex.z-dn.net/?f=%28x%20-%202%29%20%20%28x%5E2%20%2B%203x%20%2B%206%29)
![x* x^2 = x^3\\x * 3x = 3x^2\\x * 6 = 6x\\-2 * x^2 = -2x^2\\-2 * 3x = 6x\\-2 * 6 = -12](https://tex.z-dn.net/?f=x%2A%20x%5E2%20%3D%20x%5E3%5C%5Cx%20%2A%203x%20%3D%203x%5E2%5C%5Cx%20%2A%206%20%3D%206x%5C%5C-2%20%2A%20x%5E2%20%3D%20-2x%5E2%5C%5C-2%20%2A%203x%20%3D%206x%5C%5C-2%20%2A%206%20%3D%20-12)
= ![x^3 + x^2 - 12](https://tex.z-dn.net/?f=x%5E3%20%2B%20x%5E2%20-%2012)
Meaning it is simplified.
Now, put the equations together:
![3(x - 2) (x^2 + 3x + 6)\\](https://tex.z-dn.net/?f=3%28x%20-%202%29%20%28x%5E2%20%2B%203x%20%2B%206%29%5C%5C)
Hope this helps!