Question

factor completely.
27x³ - 48x

Explanation:

Step1: Find the GCF

First, find the greatest common factor (GCF) of the coefficients 27 and 48, and also note the common variable factor (if any). The GCF of 27 and 48 is 3. There is no common variable factor between \(z^3\) and \(x\). So, factor out 3 from both terms.
\(27z^3 - 48x = 3(9z^3 - 16x)\)

Step2: Check for further factoring

Now, check if \(9z^3 - 16x\) can be factored further. Since it is a binomial with different variables and no common factors, and it doesn't fit the pattern of difference of squares or cubes (as \(9z^3=(3z)^{3/2}\) which is not an integer power, and \(16x=(4x^{1/3})^3\) also not an integer power for factoring as a sum or difference of cubes in the usual sense with integer coefficients), we stop here.

Answer:

\(3(9z^3 - 16x)\)