Question 242490
Factor out 3 and then divide each term by 3.

3(x^3 - 8)

Inside the parentheses, we have the difference of cubes.

Do you know how to factor from this point on?

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I received your reply.

Here is mine.


Factor out 3 and then divide each term by 3. 
We get this: 3(x^3 - 8) 

Inside the parentheses, we have the difference of cubes.
 
We need the difference of cubes formula and it is:
 
a^3 – b^3 = (a – b)(a^2 + ab + b^2)
 
We simply plug and chug.
 
8 = 23
 
x3 – 8 becomes   x3 –  23. 
 
Are you following so far?
 
x^3 –  2^3  = (x – 2)(x^2 + 2x + 4)
 
I simply plugged x and 2 into the difference of cubes formula and simplified.
 
So, the final answer is:  3(x – 2)(x^2 + 2x + 4)
 
Guido