Determine the greatest common factor
8z^3+27
A) (2z-3)(4z^2-6z-9)
B) (2z+3)(4z^2-12z+9)
C) (2z+3)(4z^2-6z+9)
D) (2z-3)(4z^2-12z-9)
To find the greatest common factor of the given expression, we need to factor it completely.
8z^3+27 can be written as (2z)^3+(3)^3, which is in the form of a^3+b^3. This can be factored using the difference of cubes formula:
a^3+b^3 = (a+b)(a^2-ab+b^2)
Using this formula, we can factor 8z^3+27 as:
(2z+3)((2z)^2-(2z)(3)+(3)^2)
= (2z+3)(4z^2-6z+9)
Therefore, the correct answer is:
C) (2z+3)(4z^2-6z+9)