Final answer:
The statement is true for thermoset polymers, which are characterized by an extensive cross-linked network of covalent bonds that prevent the material from softening upon reheating.
Step-by-step explanation:
The statement presented suggests that a polymer will no longer soften when heat is applied due to covalent bonds along and across the linear chains. This description fits thermosets, which are polymers that once hardened, will not soften again upon heating.
Thermosets are characterized by extensive cross-linking, which creates a three-dimensional network of covalent bonds that provide mechanical strength and thermal stability. This is in contrast to thermoplastics, which can soften upon heating and can be reshaped. Thus, the statement is true for thermosets, as they do not soften once they have been fully cured or set.