Answer: It is possible to keep mums from year to year, yes. First you need to plant a variety that is considered winter hardy in your climate as they do vary in innate cold tolerance.
Spring planted mums have a better success rate than fall planted mums because they have a longer period in which to become rooted and established before the winter cold.
Mums require a full sun location. They need soil that is rich, evenly moist during the growing season, and yet also well drained. A well drained location is critical for winter survival. Planting in heavy clay soil or in a low spot will usually result in failure.
In fall after blooming, leave the stems intact or cut them down to about six inches. This offers a little protection to the crown during the winter. Mulch around the plants but not over top of them in late fall after hard freezing weather has occurred.
In spring, gradually remove the mulch. Cut the dead stems off very short. In mid spring you will (hopefully) see new growth coming up around the perimeter of the plant.
Most gardeners divide their mums every spring or every other spring to help keep the plant vigorous. Mums also require pinching several times during the spring and early summer to encourage shorter plants, denser branching and more blooms. Stop pinching by mid July.
I hope this helps.
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