Beginner question: Increasing poly density for a single side of a cube I am new to 3d-modeling, so please bear that in mind and if you find some fundamental flaw in my explanation below, do not hesitate to tell me. 

The mesh I want is a cuboid with a lot more faces on one of its sides compared to the others. I inserted a cube, scaled it and applied  transformations, subdivided it once and added a few edge loops to help subdivision. The resulting mesh then looked like this:



(Up until this point everything worked as I expected)

In order to get more polys on one of the sides I selected its four inner faces and subdivided them, the result was that adjacent faces "degenerated" into n-gons, which I want to avoid (because the target application does not like them). This is the resulting mesh, where I selected the resulting ngons using select->facesBySide:



This of course makes sense, because these adjascent faces now have more than 4 vertices, but I am not really sure how to proceed from here. I currently see only two solutions to this problem:
1) Either subdivide the whole mesh evenly (which is actually not a solution at all, because the resulting mesh will have the same poly-density on all sides)
2) Connect all the new vertices of the adjascent faces (the ngons) to a "corner vertex" by creating new edges for each, which results in a set of many ugly stretched out triangles.

Both solutions seem undesirable to me. So how would a more experienced poly-modeler approach this?

Thanks in advance!

ps. I realize that this is a beginner's questions which probably has been answered a million times. Unfortunately I did not find anything, but if you know a post or a tutorial explaining these things, it would be great if you could post the link.
I am glad you asked that question. I see many meshes from beginners with triangles or Ngons (polygons with more than 4 vertices) when it's not necessary. In most cases it's easy to change mesh density using only quads--once you know how.  The image below shows some examples to get you started.  Good luck.