Question

z^3-27 / z-3

Answer 1

A factoring technique: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
z^3 is a perfect cube
27 = 3^3 is a perfect cube.

Answer 2

We simply rewrite z^3 - 27 as (z - 3)(z^2 + 3z + 9).
We have a factor of (z-3) in both the numerator and denominator, so they may cancel (assuming \(\text{z}\ne 3\))