Bricks, Masonry, Asphalt and Concrete - Filler product required for cracked cement floor

I need to repair some .25 - 1.5 inch cracks and fractures in a 1930s cement floor. Sakrete is inadequate for this job since the floor is unstable and is moving. If Sakrete, which is inflexible, is used, it also will crack.

Can someone recommend a flexible product to fill in these cracks?

Thanks.

There are flexible products that come in a tube which are applied with a caulking gun. Your local hardware store or Home Depot will carry them.

would this same stuff work on a driveway crack, exposed to the weather? the drive is less than a year old and has a crack across the entire width of the drive thru about 5 different sections. Is this normal, the contractor won't do anything to help fix it. Thanks

Cracks in concrete are definitely normal, and there is no real fix short of tearing it out and repouring. However, it should have cracked in the control joints instead of randomly across the driveway. If the joints aren't deep enough or are spaced too far apart, then the concrete creates its own joints by cracking. There is patch material available as described above, but that's not "fixing" the crack.
As to the concrete cracking before a year was up, this is also normal. Shrinkage cracks happen within a few days of the pour, or in extreme cases within hours. That's why concrete needs to be jointed as soon as possible after pouring: to create a weak place for the crack to happen.
When concrete is poured, it is as big as it is ever going to get. As it cures and loses moisture, it shrinks. The stresses caused by the shrinking are what cause many of the cracks in new concrete. This is especially true where concrete is poured around a corner (such as against a house corner or a column.)
What is not normal or acceptable is if the concrete separates more than about 1/4 inch at the crack.