Question

Find the greatest common factor of the terms of the polynomial.

4x^3- 12x

Write your answer as a constant times a product of single variables raised to exponents.

Answer 1

For this case we must find the GCF of the following expression:

$4x ^ 3-12x$

By definition we have that the GCF of an expression is given by the greatest common factor that divides both numbers without leaving remainder.

We find the factors of 4 and 12:

$4: 1,2,4\\12: 1,2,3,4,6,12$

The GCF of both numbers is 4. Thus, the GCF of the expression is $4x$:

$4x (x ^ 2-3)$

Answer:

$4x (x ^ 2-3)$