Prove the divisibility of the following number using factoring!

7^6 + 7^5 - 7^4 by 11

X = 7^6 + 7^5 - 7^4

x = 7^4*7^2 + 7^4*7 - 7^4*1

x = 7^4 * (7^2 + 7 - 1)

x = 7^4 * (49 + 7 - 1)

x = 7^4*55

x = 55*7^4

x = 11*5*7^4

x = 11*y ... where y = 5*7^4 is an integer

Since x = 11*y, and y is an integer, this means x is a multiple of 11

So that proves 7^6 + 7^5 - 7^4 is divisible by 11