Final answer:
The greatest common factor of the expression 5x(z+8)+(z+8) is (z+8).
Step-by-step explanation:
To find the greatest common factor (GCF) of the expression (5x(z+8)+(z+8), we can factor out the common factor.
The given expression is (5x(z+8) + (z+8). Notice that both terms have a common factor of (z+8). We can factor this common term out:
(z+8)(5x + 1)
Now, the expression has been factored into the product of the common factor (z+8) and the remaining factor 5x + 1. The GCF is (z+8), and the factored expression is (z+8)(5x + 1).