You're right that you need to factor. But, you shouldn't have x terms in your choice of delta. Try getting a bound on the big factor (x^4+...) by making a bound on x.
Indeed. But don't forget that you want an upper bound, and you certainly have that x< |a|+1 So, use this to get aqn upper bound on the big polynomial factor, take delta to be the minimum of 1 and epsilon/(bound on poly)