Question

Question 2 (5 points)

Answer 1

Answer:

The greatest common factor is 8xyz

Step-by-step explanation:

To find the greatest common factor of an expression involving numbers and variables, we find each greatest common factor separately.

Numbers:

48, 24 and 56.

We find the greatest common factor factoring them simultaneously while all can be factored by the same number. The GCF is the multiplication of the factors. So

48 - 24 - 56|2

24 - 12 - 28|2

12 - 6 - 14|2

6 - 3 - 7|

They cant be factored by the same factors anymore, so the numeric GCF is 8.

Variables:

For each variable, the GCF will be the lowest exponent.

Variable x: We have exponents 1, 2 and 2. So the GCF is $x^1 = x$

Variable y: We have exponents 3, 3 and 1. So the GCF is $y^1 = y$

Variable z: We have exponents 1, 1 and 1. So the GCF is $z^1 = z$

The greatest common factor is:

$8*x*y*z = 8xyz$