Which type of polymer does not melt when heated due to its strong covalent crosslinks?

The correct choice refers to thermosetting polymers, which are characterized by their strong covalent crosslinks. These crosslinks create a rigid structure that does not soften or melt when subjected to heat. Instead of melting, thermosetting polymers will undergo thermal decomposition when heated to high temperatures. This property makes them ideal for various applications, such as in adhesives, coatings, and electrical insulations, where heat resistance and structural integrity are vital.

In contrast, thermosoftening polymers can be melted and reshaped upon heating, due to their linear or branched structures without significant crosslinking. Elastomers, although they can return to their original shape after being stretched, still contain some crosslinking but not to the extent that would prevent melting. Polyethylene, while it is a polymer, is a type of thermosoftening polymer and does not fit into the category of materials that resist melting due to crosslinked structures. Therefore, the unique properties of thermosetting polymers, due to their covalent crosslinks, explain why this is the correct answer.