Question

one of the factors of 6x^3 - 864x is
4
x^2
x + 12
x - 8

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor of \(6x^{3}\) and \(864x\). The GCF of 6 and 864 is 6, and the GCF of \(x^{3}\) and \(x\) is \(x\). So, \(6x^{3}-864x = 6x(x^{2}-144)\).

Step2: Factor the difference of squares

We know that \(a^{2}-b^{2}=(a + b)(a - b)\). Here, \(a = x\) and \(b = 12\) since \(x^{2}-144=x^{2}-12^{2}\). So, \(6x(x^{2}-144)=6x(x + 12)(x - 12)\).

Answer:

C. \(x + 12\)