Can someone please show me how to factor $6q(7(6q)^2 +5)$ to show that it is a multiple of 6? I'm working on a division algorithm problem, and I understand concepts of div alg but I really don't have much experience factoring and I can't find any good sources on learning this type of thing. Thank you in advance.
You already have shown it:
The quantity: $$6q(7(6q)^2 +5)$$
Is divisible by $6$ because of the quantity $6q$ in front of the parenthesis. The $6$ implies that the polynomial is divisible by $6$.