[tex]GCF = 5(x+7)^2[/tex]
Solution:
Given that,
We have to find the greatest common factor
[tex]5(x+7)^4\\\\35(x+7)^2\\\\15(x+7)^3[/tex]
First find the GCF of numbers 5, 35 and 15
Find the GCF of 5, 35 and 15
The factors of 5 are: 1, 5
The factors of 15 are: 1, 3, 5, 15
The factors of 35 are: 1, 5, 7, 35
Then the greatest common factor is 5
Now find the GCF of variables
[tex](x+7)^4\\\\(x+7)^2\\\\(x+7)^3[/tex]
Here, the common factor is [tex](x+7)^2[/tex]
Thus, GCF for given expression is:
[tex]GCF = 5(x+7)^2[/tex]