How is an approximation Factor different than time-complexity? I have heard, for example, of polynomial algorithms with exponential factors, what does that mean? Does that mean it is not technically in polynomial time?
What is an Approximation Factor?
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Don't have enough reputation points, hence posting as answer.
Perhaps your use of factor in two different senses is the source of the confusion. Time is but one factor out of many possible complexity factors, such as storage, bandwidth, etc. Exponential factors in the case of polynomial algorithms refer to the factors of the terms in the mathematical equation. They do not necessarily imply time as a factor, but they do not exclude it either. It depends on what the algorithm is modeling.