x^5 is definitely the greatest common factor of x because:
x^5 * 1 = x^5
x^5 * x^2 = x^7
x^5 * x^3 = x^8
the greatest common factor of 110 and 70 and 60 should be 10 because:
10 * 11 = 110
10 * 7 = 70
10 * 6 = 60
there is no other common factor of 1 and x^2 and x^3 so they're relatively prime compared to each other.
there is no other common factor of 11 and 7 and 6 so they're relatively prime compared to each other.
the common factor appears to be 10x^5
your terms of 110x^5 + 70x^7 + 60x^8 become
10x^5 * (11 + 7x^2 + 6x^3)
note that 10x^5 * 11 is equal to 110x^5
note that 10x^5 * 7x^2 is equal to 70x^(5+2) which is equal to 70x^7
note that 10x^5 * 6x^3 is equal to 60x^(5+3) which is equal to 60x^8
